This book opens up new research areas in theoretical and computational number theory, numerical approximation, dynamical systems, quantum dynamics, and the physics of numbers. With a strong emphasis on applications: Each chapter is self-contained. Yo

(Credit: René Ramos; Nintendo; Sora)The Best Games on Every Platform Animal Crossing: New Horizons Animal Crossing: New Horizons (for Nintendo Switch) 4.0 Excellent No game may end up defining 2020 more than Animal Crossing: New Horizons. Nintendo’s adorable life simulator has always had its fans. However, with the real world under lockdown, countless players have flocked to their own virtual islands to find community. Paying a mortgage to a raccoon is a small price to pay for the freedom to relax in your own social life again. Advance Wars 1+2: Re-Boot Camp Advance Wars 1 + 2: Re-Boot Camp 4.0 Excellent Fire Emblem isn't Nintendo's only awesome strategy series. If you prefer soldiers and tanks over knights and horses, check out Advance Wars and its terrific turn-based tactics. This remake includes campaigns from the first two Game Boy Advance games, offering hours upon hours of brilliantly designed missions. You can also design your own maps and play against friends online. Advance Wars 1 + 2: Re-Boot Camp review ARMS ARMS (for Nintendo Switch) 4.0 Excellent ARMS is Nintendo's newest take on the fighting game genre. It combines cartoonish aesthetics, sci-fi weapons, and arm-stretching boxing into an accessible, offbeat fighter with a lot of variety. It's a polished, fun, competitive game that bears more than a passing visual similarity to Splatoon. Though time will tell if ARMS gains any momentum within the esports scene, the game offers plenty of opportunity to swing fists at your friends. Bayonetta 2 Bayonetta 2 (for Nintendo Switch) 4.5 Excellent Bayonetta 2 is another fantastic game that launched on the wrong system. Years later its initial release, Bayo 2 still stands as one of the best action games out there, and now that it's been ported from the Wii U to the Switch it can get the attention and devotion it deserves. Tight controls, robust challenge, and plenty of style make this stand out as a pinnacle of action games. Bayonetta 3 Bayonetta 3 (for Nintendo Switch) 4.5 Excellent Just when you thought Bayonetta couldn’t get any more bewitching, PlatinumGames delivers an absolute master class on video game action with Bayonetta 3. Besides Bayonetta’s familiar punches, kicks, and guns, you can further expand her combat options by summoning giant demons and directing their attacks. Meanwhile, the multiversal story is ridiculous, even by Bayonetta standards. Bloodstained: Ritual of the Night Bloodstained: Ritual of the Night (for Nintendo Switch) 4.0 Excellent If Bloodstained: Ritual of the Night's story of a demonic castle and a lone savior sounds incredibly familiar, it should: the game was spearheaded by Koji Igarashi, the big brain behind many revered Castlevania games. Bloodstained is an excellent Castlevania game in everything but name, hitting the same beats Symphony of the Night, Aria of Sorrow, and Order of Ecclesia did. If you're thirsty for a new, enjoyable Castlevania-like game that calls back to before Lords of Shadow rebooted the series and Mirror of Fate completely failed to capture any of its luster, this is the game for you. Bayonetta Origins: Cereza and the Lost Demon 4.0 Excellent Bayonetta Origins: Cereza and the Lost Demon isn’t a hard-hitting, nonstop action game like the main Bayonetta trilogy. Instead, this is a relatively relaxed adventure game full of puzzles and gorgeous storybook visuals. Young witch Cereza teams up with a young demon, Cheshire, to tackle challenges neither could complete alone. Although the combat isn’t quite as complex as in the mainline Bayo games, there’s still plenty of flair to the faerie fights. Bayonetta Origins: Cereza and the Lost Demon review Bravely Default II Bravely Default II (for Nintendo Switch) 4.0 Excellent Modern Final Fantasy games have become their own beasts, but games like Bravely Default II remind us why we fell in love with those classic Square Enix JRPGs. In battle, you can either perform multiple actions at once (Brave) or wait to save up for later turns (Default), which opens up many strategic possibilities. On Switch, the diorama world looks more beautiful and nostalgic than ever. Cadence of Hyrule: Crypt of the NecroDancer Cadence of Hyrule: Crypt of the NecroDancer (for Nintendo Switch) 4.0 Excellent Crypt of the NecroDancer was a surprise indie hit in 2015, catching gamers' eyes and ears with its combination of roguelike randomized dungeon exploration with rhythm game beat-keeping. It hit the Nintendo Switch in 2018, and now it's back in a new and much more Nintendo-specific form: Cadence of Hyrule: Crypt of the NecroDancer, a title that injects rhythm game mechanics into The Legend of Zelda. This Switch game seamlessly combines Zelda and Crypt of the NecroDancer, creating a surprisingly accessible and thoroughly enjoyable experience played to the beat of Zelda's classic and music. Cassette Beasts 4.0 Excellent Pokémon doesn't have a monopoly on monster catching. Cassette Beasts is a stylish, indie RPG that puts its own spin on collecting creatures and pitting them against each other in combat. The open world has many quests, the fighting mechanics have the extra depth that experienced players crave, and the story veers off in cool, surreal directions. Most importantly, there are some great monster designs, like ghostly sheep and living bullets. Cassette Beasts review Clubhouse Games: 51 Worldwide Classics Clubhouse Games: 51 Worldwide Classics (for Nintendo Switch) 4.0 Excellent Forget fancy new video games. Sometimes you just want to play chess, solitaire, or one of the other virtual vintage games that make up this classic compilation. Not only is this a convenient way to play some of history’s most enduring games with friends, but Clubhouse Games: 51 Worldwide Classics does a great job educating you on that history, including the fascinating early Hanafuda history of Nintendo itself. Game Builder Garage Game Builder Garage (for Nintendo Switch) 4.5 Excellent If you thought Super Mario Maker was a great way to learn about game development, give Game Builder Garage a spin. This incredibly powerful 3D game creation tool lets you make anything from platformers to racing games to puzzle mysteries. Thorough, friendly tutorials explain the robust “Nodon” coding language, so even novices can create hitboxes and manipulate the Z-axis like pros. Donkey Kong Country: Tropical Freeze Donkey Kong Country: Tropical Freeze (for Nintendo Switch) 4.0 Excellent The Switch has gotten a reputation as a machine for game ports, and there's nothing wrong with that. The Wii U wasn't the massive hit the Wii was, but it still had several excellent games that went underappreciated in their time. Donkey Kong Country: Tropical Freeze is one of them, a sequel to Donkey Kong Country Returns with even more challenge and variety. The Switch version of this game adds Funky Kong Mode, an easier setting and new playable character (Funky Kong himself) that makes the surprisingly brutal platforming feel a little less punishing. Hades Hades (for Nintendo Switch) Hades takes the punishing and divisive roguelike genre and masterfully twists it into one of the year's most addictive games. Fighting your way out of the Greek underworld with randomly changing skills and weapons feels incredible. The family drama at the game’s core gives you that extra narrative push to keep going. Plus, everyone is smoking hot. Indivisible Indivisible (for Nintendo Switch) While many role-playing games draw their influences from Western folklore, even RPGs made in Japan, Indivisible carves out a unique identity with a fresh Southeast Asian flavor. The 2D animation is exquisite, as we would expect from the developer of Skullgirls. Gameplay is a mix of nonlinear spaces to explore and enemies to defeat in tactical battles. Of the two types of play, the exploration sections impress us more. In these bits you find your way forward by using an axe to fling yourself up walls or by shooting arrows to blind sentries. That's just more satisfying than the frantic messes the fights, caught awkwardly between turn-based and real-time combat, can turn into.   Kirby's Return to Dream Land Deluxe Kirby’s Return to Dream Land Deluxe (for Nintendo Switch) 4.5 Excellent Kirby’s Return to Dreamland is a traditional, side-scrolling adventure compared to Kirby’s more radical outings. Still, it’s an excellent showcase of what makes even a normal Kirby game irresistible. This Deluxe version enhances the Wii co-op classic with a sweet, new art style; extra powers; and an original epilogue. Kirby’s Return to Dream Land Deluxe (for Nintendo Switch) review Kirby and the Forgotten Land Kirby and the Forgotten Land (for Nintendo Switch) 4.0 Excellent Kirby and the Forgotten Land finally gives the pink puffball the epic 3D adventure that Mario, Link, and Samus got years ago. Float through the skies in creative levels bursting with secrets. Upgrade familiar powers, such as hammers and swords, into formidable new forms. Or just sit back and marvel at how Nintendo made the post-apocalypse look so cute. Kirby Star Allies Kirby Star Allies (for Nintendo Switch) 4.0 Excellent Kirby games are always fun. Whether they're the simple platformers like Kirby's Adventure or weirdly gimmicky experiences like Kirby's Dream Course, every first-party experience with Nintendo's pink puff ball has been enjoyable. Kirby Star Allies is no different, with a lighthearted campaign filled with colorful friends and abilities, surprisingly challenging extra modes to unlock, and support for up to four players at once. Get on the Friend Train! The Legend of Zelda: Breath of the Wild The Legend of Zelda: Breath of the Wild (for Nintendo Switch) 4.5 Excellent Hyrule is in danger again, and Link must save it. That's been the theme for nearly every Legend of Zelda game, and it's still the case in The Legend of Zelda: Breath of the Wild. The series' basic premise and Link/Zelda/Ganon dynamic are present, but nearly everything else is different. The classic Zelda dungeon-exploration structure is replaced by a huge open world that's filled with destructible weapons, monsters, puzzles, and quests. Breath of the Wild's scope is one previously unseen in the Zelda series, and Nintendo executes the adventure-filled world with aplomb. The Legend of Zelda: Echoes of Wisdom The Legend of Zelda: Echoes of Wisdom - Nintendo Switch, Nintendo Switch – OLED Model, Nintendo Switch Lite 4.5 Excellent The Legend of Zelda: Echoes of Wisdom turns Nintendo's epic franchise on its head in more ways than one. Instead of the swordsman, Link, you play as Princess Zelda. Likewise, you don't directly attack enemies; you summon useful items and foes to aid you on the mission. The game takes the creative, improv spirit of Breath of the Wild and applies it to a classic 2D top-down Zelda adventure with delightful results. Plus, it just looks adorable. The Legend of Zelda: Echoes of Wisdom - Nintendo Switch, Nintendo Switch – OLED Model, Nintendo Switch Lite review The Legend of Zelda: Skyward Sword HD The Legend of Zelda: Skyward Sword HD (for Nintendo Switch) 3.5 Good No Zelda games are terrible, but no game polarizes the fan base quite like Skyward Sword. Fortunately, this HD remaster speeds up the pacing, enhances the graphics, and offers a button-based control scheme if you don’t care for motion controls. The structure feels especially linear in a post-Breath of the Wild world, but Zelda’s origin story is still worth experiencing. The Legend of Zelda: Tears of the Kingdom The Legend of Zelda: Tears of the Kingdom - Nintendo Switch, Nintendo Switch (OLED Model), Nintendo Switch Lite 5.0 Outstanding At launch, it was tough to imagine the Switch ever getting another game as good as Breath of the Wild. But years later, The Legend of Zelda: Tears of the Kingdom delivers everything we could have possibly wanted and more in this direct sequel to one of the greatest games ever made. Exploring the skies and underground caves makes Hyrule more vast than ever. New powers let you break the world apart and rebuild it as you see fit. Tears of the Kingdom is an irresistible, hypnotic adventure, and an absolute must-play for all RPG fans. The Legend of Zelda: Tears of the Kingdom - Nintendo Switch, Nintendo Switch (OLED Model), Nintendo Switch Lite review Lego Star Wars: The Skywalker Saga Lego Star Wars: The Skywalker Saga (for Nintendo Switch) 4.0 Excellent Who knows what the future holds for Star Wars, but Lego Star Wars: The Skywalker Saga provides a terrific toybox take on Episodes I-IX. The Lego recreations of all nine movies gives you plenty to experience as you blast baddies and solve Force puzzles. But what really makes this game so special is how it turns the entire Star Wars galaxy into an open world to explore, whether it’s on colorful planets or through the vastness of outer space in your trusty starfighter. Lego Star Wars: The Skywalker Saga (for Nintendo Switch) review Luigi's Mansion 3 Luigi's Mansion 3 - Nintendo Switch Standard Edition What started as a weirdly specific parody of Ghostbusters and Resident Evil has become of one the finest Mario spin-off adventures. Luigi’s spooky journey throughout a haunted hotel is arguably the most visually stunning game on the Nintendo Switch. Along with sucking up ghosts, you can now slam them (back) to death and shoot plungers to pull apart the scenery. Your greatest, and grossest, tool has to be Gooigi. This slimy green doppelgänger expands your puzzle-solving powers and provides an easy option for younger co-op partners. Lumines Remastered Lumines Remastered (for Nintendo Switch) 4.5 Excellent Puyo Puyo Tetris is great for classic, competitive block-dropping, but it's a bit overly perky and anime-ish to really relax to. Lumines Remastered is the ultimate chill-out block-dropper, syncing the mesmerizing pattern matching to dozens of hypnotic electronic and trance tracks. Load it on your Switch, put on your favorite headphones, and space out while you build huge combos. Mario & Luigi: Brothership Mario & Luigi: Brothership - Nintendo Switch, Nintendo Switch – OLED Model, Nintendo Switch Lite 4.0 Excellent Mario & Luigi: Brothership revives a Mario RPG subseries as a grand nautical adventure. The plumbers sail the seas, reconnecting scattered islands and battling foes with familiar, frenetic turn-based combat. On Nintendo Switch, the visuals and animations turn Mario and Luigi into cartoon-like characters. Mario & Luigi: Brothership - Nintendo Switch, Nintendo Switch – OLED Model, Nintendo Switch Lite review Mario + Rabbids: Kingdom Battle Mario + Rabbids: Kingdom Battle (for Nintendo Switch) 4.0 Excellent Before Minions, there were Rabbids, Ubisoft's manic, sublingual, noseless horde spawned from Rayman: Raving Rabbids. Then the weird, bug-eyed, rabbit-like creatures caused havoc in their own game series. Now, they're running around Mario's stomping grounds in Mario + Rabbids: Kingdom Battle. This strategy-RPG combines two cartoonish worlds with satisfyingly deep, XCOM-like gameplay for a very fun and strange experience. It's a combination of styles that work much, much better than you'd expect. Mario + Rabbids Sparks of Hope Mario + Rabbids Sparks of Hope (for Nintendo Switch) 4.0 Excellent Mario + Rabbids Kingdom Battle proved that these two mascots could come together for excellent, approachable tactics gameplay. Sparks of Hope is more of the same, but even better. Equipping Sparks lets you further customize your squad’s strategic abilities. Wide open levels provide entertaining exploration between the skirmishes. Mario Golf: Super Rush Mario Golf: Super Rush (for Nintendo Switch) 4.0 Excellent Leave it to Mario to find a way to make golf games feel fresh again. Mario Golf: Super Rush’s standout gimmick has golfers teeing off all at once, and then physically running across the course to take their next shot. You still have to plan smart strokes, but you also need to keep an eye on the clock. The lengthy, single-player adventure teaches you the ropes before you head online to face real challengers on the green. Mario Kart 8 Deluxe Mario Kart 8 Deluxe (for Nintendo Switch) 4.5 Excellent Mario Kart 8 stood out as the best-looking Mario Kart game yet when it came out on the Nintendo Wii U. Instead of making a new Mario Kart for the Nintendo Switch, Nintendo brought Mario Kart 8 to its new game system. In the process, Nintendo threw in both previously released DLC packs and made some few welcome changes to its multiplayer options, justifying the game's full retail price. Mario Kart 8 Deluxe is the most robust game in the series so far, and with the optional portability of the Switch, it ranks as a must-own title. Mario Strikers: Battle League Mario Strikers: Battle League (for Nintendo Switch) 4.0 Excellent Mario has played many sports throughout the years, but Mario Strikers: Battle League gives us the arcade soccer chaos fans have craved for more than a decade. It features fast-paced action, while allowing for depth and skill should you choose to push yourself. Customize your characters with stat-changing gear. Join online clubs to compete in ongoing seasons. And no one animates the Mario universe with as much style and attitude as the developers at Next Level Games. Mario Strikers: Battle League (for Nintendo Switch) review Mario Tennis Aces Mario Tennis Aces (for Nintendo Switch) 4.0 Excellent You don't need to be a sports fan to enjoy Nintendo sports games. If a sport has "Mario" in front of it, it's probably going to be a fun, very unrealistic romp instead of a serious simulation. Mario Tennis Aces is an exciting tennis game not because of any realistic physics, but because of fast, responsive gameplay and strategic mechanics that make matches feel more like rounds in a fighting game than tennis sets. Marvel vs. Capcom Fighting Collection: Arcade Classics Marvel vs. Capcom Fighting Collection: Arcade Classics - Nintendo Switch 4.0 Excellent Marvel vs. Capcom Fighting Collection: Arcade Classics lets you finally relive six legendary 2D fighters starring Marvel superheroes and Capcom icons. From the humble X-Men: Children of the Atom to the over-the-top Marvel vs. Capcom 2, this is vital fighting game history. An art gallery, modern control options, rollback netcode, and the underrated Punisher beat 'em up sweeten the deal. Marvel vs. Capcom Fighting Collection: Arcade Classics - Nintendo Switch review Metal Slug Tactics Metal Slug Tactics (for Nintendo Switch) Metal Slug Tactics trades the mainline series' fast-paced running and gunning for methodical, turn-based strategy gameplay. Still, it's just as action-packed as ever. Line up your units for devastating sync attacks. Enjoy the beautiful old-school sprite work. Plan your turns, hop into a giant tank, and obliterate foes. Metroid Dread Metroid Dread (for Nintendo Switch) 4.5 Excellent After nearly 20 years, Metroid Dread brings Samus Aran back to her 2D, bounty hunting roots for the true Metroid 5. In it, you explore a dense, dangerous new planet full of powers to pick up and enemies to eliminate. From uncompromising boss battles to terrifying chases, Dread more than lives up to its subtitle. If there's anyone strong enough to take down the terror, it's Nintendo's leading lady. Metroid Prime Remastered 5.0 Outstanding Metroid Prime is one of the best games ever made. It takes Super Metroid’s brilliant exploratory action and perfectly translates it to 3D with immaculate level design and immersive first-person shooting. This remaster, which ventures into the remake territory, includes everything that worked in the original, and ups the presentation to modern, beautiful standards. Plus, you can now play with dual-stick controls. Bring on Metroid Prime 4. Metroid Prime Remastered review Miitopia Miitopia (for Nintendo Switch) 3.5 Good Miis can do more than just play Wii Sports. In Miitopia, you use Nintendo’s cartoon caricatures to cast yourself, friends, and family as heroes and villains in a fast-paced, whimsical role-playing game. Turn yourself into a brave knight, while your buddy supports you as a pop star. The joke can’t quite sustain the whole runtime, but Miitopia is wildly entertaining.   Monster Hunter Stories 2: Wings of Ruin Monster Hunter Stories 2: Wings of Ruin (for Nintendo Switch) 4.0 Excellent If traditional Monster Hunter is just too intense for you, Monster Hunter Stories 2 lets you experience this cutthroat world as a turn-based JRPG. Befriend monsters and take them into battle. Hatch eggs to expand your menagerie. Strategic battles draw upon familiar Monster Hunter concepts. And, of course, Rathalos is here. New Pokemon Snap New Pokemon Snap (for Nintendo Switch) 4.0 Excellent The beloved Nintendo 64 spin-off finally gets the update it deserves. Instead of capturing Pokemon and forcing them to battle, New Pokemon Snap asks you to take beautiful photos of Pikachu and friends in their natural surroundings. The on-rails gameplay feels like a nonviolent version of a light gun game. The gorgeous graphics will inspire you to share your best pics online for the world to see. Nickelodeon All-Star Brawl Nickelodeon All-Star Brawl (for Nintendo Switch) 4.0 Excellent Imagine Super Smash Bros., but instead of playing as video game mascots, you control beloved cartoon characters beating each other senseless. That's Nickelodeon All-Star Brawl. From SpongeBob SquarePants to Ren and Stimpy to the Teenage Mutant Ninja Turtles, the roster covers all eras of Nicktoon nostalgia. Beyond the ironic meme potential, "Nick Smash" features genuinely fantastic gameplay made by a team clearly passionate about this particular form of "platform fighting" games. Nickelodeon All-Star Brawl (for Nintendo Switch) review Nintendo Labo Toy-Con 01 Variety Kit Nintendo Labo Toy-Con 01 Variety Kit (for Nintendo Switch) 5.0 Outstanding Labo is a weirder concept than the Switch itself. It's based around building cardboard "Toy-Cons" in which you place the Switch's components to let you do new things with them. It's also surprisingly functional, entertaining, and educational. The Nintendo Labo Variety Kit has all of the parts you need to build several different Toy-Cons like a piano and motorcycle handlebars, and walks you through every step of the process. Just building the Toy-Cons is fascinating, but the Toy-Con Garage mode adds surprisingly robust programming options to let you create your own remote-controlled creations. Nintendo Labo: VR Kit 4.5 Excellent It took over 20 years, but Nintendo finally got over its fear of virtual reality after the disastrous Virtual Boy. The Labo VR Kit lets you build your own VR headset that uses the Nintendo Switch and a set of lenses to create a stereoscopic image, and then insert that headset into different Toy-Con controllers to play a variety of games. That's already a ton of fun for $79.99 (or $39.99 for a starter set that only includes one Toy-Con to build instead of five). Add a programming environment on top that lets you create your own 3D games, and you have an impressive package. No More Heroes III No More Heroes III (for Nintendo Switch) 4.0 Excellent No More Heroes III, like the other games in Suda51’s hack-and-slash trilogy, is a punk art game. Sure, some parts may be “bad,” like the technical jank or empty open worlds. But it’s all in service of larger commentary on everything from schlocky movies to wrestling fandom to the video game industry itself. Plus, cutting aliens down to size feels legitimately fantastic, and really that’s what matters.  Penny's Big Breakaway 4.0 Excellent The creators of Sonic Mania deliver a new indie 3D platformer that feels like a forgotten Sega classic. Use your trusty yo-yo to swing and roll through colorful, tightly designed levels that test your momentum control. Bosses and other enemies are sometimes more annoying than fun, but the movement mechanics are a joy to master. Penny's Big Breakaway review Pikmin 3 Deluxe Pikmin 3 Deluxe (for Nintendo Switch) 3.5 Good Pikmin isn’t the most recognizable Nintendo franchise, but the approachable real-time strategy game carries as much magic as Mario and Zelda. This Wii U port offers more missions and ways to control your army of cute plant creatures. The campaign's local, co-op play opens all kinds of new strategies, too. Veterans of previous Pikmin wars may have seen most of this content before, but Pikmin newcomers should absolutely jump into this tiny, tactical, and tactile world. Pikmin 4 Pikmin 4 (for Nintendo Switch) 4.5 Excellent Pikmin has always been good, but the quirky real-time strategy game has never broken out of its cult status over the past 20 years. Hopefully, that all changes with Pikmin 4. The biggest and best Pikmin game yet, Pikmin 4 gives you new Pikmin to command, a cute and customizable dog companion, and many gorgeous areas to strategically explore whether above ground or in countless caves. The multiplayer could be better, but Pikmin 4 is a top-tier Nintendo game everyone should play. Pikmin 4 (for Nintendo Switch) review Pizza Tower Pizza Tower feels like a fever dream of 1990s cartoons, internet memes, and retro Wario Land games. Don’t let his pudgy exterior fool you. Protagonist Peppino Spaghetti has many incredibly fast and fluid platforming tools, including dashing and wall-running. You’ll need to master those tools to beat levels as fast as possible, without losing your mind. Pokemon Legends: Arceus Pokemon Legends: Arceus (for Nintendo Switch) 3.5 Good Pokemon Legends: Arceus finally gives the Pokemon franchise a long-awaited refresh. Taking place in the distant past of Diamond and Pearl’s Sinnoh region, Arceus lets you capture and study wild Pokemon in a world where humans still fear the creatures. Vast open fields, revamped battle mechanics, and an utterly addictive approach to exploration create the most immersive Pokemon experience yet. Pokemon Let's Go, Pikachu/Eevee! Pokemon: Let's Go, Eevee! 4.0 Excellent If the traditional Pokemon RPGs are still just a bit too complex for you, consider the casual adventures Pokemon Let's Go Pikachu and Let's Go Eevee. This duo remakes the first-generation Pokemon Yellow, with bright, colorful, HD graphics, and a new capture mechanic based on Pokemon Go. In addition, there are trainer battles and turn-based combat for people who dig classic Pokemon. Pokémon Scarlet and Violet Pokémon Scarlet - Nintendo Switch 4.0 Excellent Pokemon Sword and Shield and Pokemon Legends: Arceus experimented with expansive zones, but Pokémon Scarlet and Violet finally turns the monster-catching game into an open-world RPG. As we always suspected, the addictive Pokémon formula works brilliantly when you can go wherever you want, exploring towns and catching whatever monsters you encounter. Lingering technical issues keep it from reaching its full potential, but this is Pokémon's shining future. Pokemon Sword/Shield Pokemon Sword (for Nintendo Switch) 4.0 Excellent Pokemon Let’s Go Pikachu and Eevee were a nice warmup, but Pokemon Sword and Shield are the real home console Pokemon games we’ve been looking forward to playing. Travel across big, open landscapes to capture even bigger Pokemon. New expansions packs in 2020 give trainers even more regions to explore and more Pokemon to battle without having to buy a third version. The Pokedex will be complete before you know it.  Prince of Persia: The Lost Crown 4.5 Excellent Prince of Persia returns to its 2D roots with The Lost Crown, a standout entry in the crowded modern Metroidvania market. Everything just clicks. The massive map is a joy to explore. Clever puzzles make the most of inventive abilities. Deep combat systems allow satisfying expression. Challenging DLC further expands the adventure. And the presentation combines Persian flair with anime exuberance. Prince of Persia: The Lost Crown review Pokemon Unite Pokemon Unite (for Nintendo Switch) 3.5 Good If you’re curious about the MOBA genre, but scared of esports heavy-hitters like Dota 2 and League of Legends, then Pokemon Unite is the perfect place to get started. Two teams of five Pokemon battle each other in real-time to score goals across the map. This free-to-play game is also coming soon to mobile, so you’ll find plenty of aspiring Pokemon masters to challenge. Puyo Puyo Tetris Puyo Puyo Tetris (for Nintendo Switch) 4.5 Excellent Practically everyone in North America has heard of Tetris. Far fewer have heard of Puyo Puyo. Both are block-dropping puzzle games, but while Tetris has been Tetris for decades, Puyo Puyo has had many different tweaks and name changes in attempts to appeal to the west. It came out first as Puyo Pop, then received different licensed incarnations, such as Puzzle Fighter and Dr. Robotnik's Mean Bean Machine. Now, Puyo Puyo is making its mark here, thanks to Sega and a double-billing with Tetris. The pairing results in a title that's plump with game modes, unlockables, and solo and multiplayer options. Red Dead Redemption Red Dead Redemption (for Nintendo Switch) Grand Theft Auto put Rockstar Games on the map, but for many the team's true masterpiece is the epic, open-world Western saga known as Red Dead Redemption. John Marston's cowboy odyssey has the scathing tone you'd expect from the developer, but it also has heart and a sense of tragedy. The Nintendo Switch version perfectly maintains the original gameplay experience, from stylish shootouts to riding your horse across the empty desert. It also includes the Undead Nightmare DLC. Finally, a version of Red Dead you can play in a tent under the stars. Rebel Galaxy Outlaw Rebel Galaxy Outlaw (for Nintendo Switch) Rebel Galaxy Outlaw has enough action-packed, visually dazzling spaceship dogfights to excite any Star Fox fan. The real joy, however, is in the quieter moments, when you act out your galactic trucker fantasies by carrying cargo from space stations named after Texas towns. Improving your ship is a bit of a grind, but it’s a rewarding one. If you get bored, you can always shoot down pirates—or become one yourself. Rocket League Rocket League (for Nintendo Switch) Rocket League is soccer, with remote controlled cars and funny hats. It's amazing how compelling a game can be when the entire point of it is to use a car to knock a ball into a goal, but Rocket League nails it. Wild physics, colorful visuals, and simple game types you can keep coming back to while challenging friends and strangers make this one of the best pseudo-sports games on the Switch. Shovel Knight: Treasure Trove Shovel Knight: Treasure Trove (for Nintendo Switch) Platforming excellence comes to the Nintendo Switch courtesy of Yacht Club Games' Shovel Knight: Treasure Trove. This downloadable package includes the original Shovel Knight, one of 2014's top titles, as well as all the previously released DLC including the Plague of Shadows and Specter of Torment campaigns. If you long for some retro, 2D action, Treasure Trove a a game that you should not miss. Splatoon 3 Splatoon 3 (for Nintendo Switch) 4.0 Excellent Splatoon 3 isn't much different than Splatoon 2 (which in turn wasn't much different from Splatoon 1). However, no other online team-based shooter delivers an experience quite like this. Inking the ground, splatting opponents, and transforming from squid to kid never felt this good. The wealth of solo, cooperative, and competitive modes will keep you busy. Keep the party going with the excellent, roguelike DLC Side Order. Splatoon 3 (for Nintendo Switch) review Street Fighter 30th Anniversary Collection Street Fighter 30th Anniversary Collection (for Nintendo Switch) Street Fighter has been the biggest name in fighting games for decades, and Capcom is proud of that fact. While it really got going with Street Fighter II: The World Warrior, the Street Fighter 30th Anniversary Collection lets you play the original Street Fighter in all of its genre-building glory. And, after you realize how bad that first attempt was, you can play the much better sequels like Super Street Fighter II, Street Fighter Alpha 3, and Street Fighter III: Third Strike. You're looking at a dozen games in this collection, with loads of extra content like soundtracks and sprite data. Streets of Rage 4 Streets of Rage 4 (for Nintendo Switch) Streets of Rage 4 pounds life back into the dead sidescrolling beat ‘em up genre. The gameplay may not have progressed that much since Sega’s trilogy in the 1990s, but taking down hordes of goons with your fists has never looked better thanks to a thoroughly modern illustrated art style. A risky new mechanic that burns health to power special moves, unless you avoid getting hit, adds some fighting-game flair.  Super Bomberman R Super Bomberman R (for Nintendo Switch) 3.5 Good Bomberman's return to console gaming was one of the most surprising moments in the Nintendo's January 2017 Switch game showcase. Considering that the little guy's now the property of Konami, a company that's more known for killing P.T. and warring with Metal Gear maestro Hideo Kojima than making video games, it was shocking to see Super Bomberman R announced as a Nintendo Switch launch title. Thankfully, this newest entry in the beloved, bomb-tossing franchise keeps the series' simple and addicting core gameplay intact, and adds tons of modes, collectible items, and characters to keep things fresh. Super Mario 3D All-Stars Super Mario 3D All-Stars (for Nintendo Switch) 3.5 Good This classic Mario collection combines Super Mario 64, Super Mario Sunshine, and Super Mario Galaxy. They may not have received the radical visual overhaul of the original Super Mario All-Stars, but these are still three of the finest 3D platformers ever made—now playable in HD and on the go. Nintendo says this collection is a limited release, so get it while you can. Super Mario 3D World + Bowser's Fury Super Mario 3D World + Bowser's Fury (for Nintendo Switch) 4.5 Excellent Super Mario 3D World seamlessly blends the free-roaming, open-ended platforming of Mario 3D’s adventures with the concentrated multiplayer mayhem of his latest 2D romps. It was great on Wii U, and now it's even better on Nintendo Switch. However, this package’s real star is Bowser’s Fury, an ambitious spin-off that reimagines what an open-world Mario game can be. Super Mario Bros. Wonder Super Mario Bros. Wonder - Nintendo Switch 4.5 Excellent In the beginning, all Super Mario games were wonderful 2D sidescrollers that dazzled us with their sheer imagination. But as Mario set his sights on 3D heights, the New Super Mario Bros. series turned 2D Mario into a safe and bland nostalgia franchise. No more! Super Mario Bros. Wonder fills 2D Mario to the brim with whimsy, creativity, and joyful confusion. Turn levels into psychedelic dreamscapes! Customize your abilities! Compete against friends online! Transform into an elephant! You can do all of this and more in Super Mario Bros. Wonder. Super Mario Bros. Wonder - Nintendo Switch review Super Mario Maker 2 Super Mario Maker 2 (for Nintendo Switch) 4.5 Excellent Super Mario Maker 2 is a welcome update to the original Super Mario Maker. It adds a new skin, new themes, and plenty of new tools for making more creative and challenging Mario levels. You can create levels based on the graphics and mechanics of Super Mario Bros., Super Mario Bros. 3, Super Mario World, and New Super Mario Bros., just like in the previous Super Mario Maker. These levels can use one of 10 different themes: Ground, Sky, Underground, Forest, Underwater, Ghost House, Desert, Airship, Snow, and Castle. Sky, Forest, Desert, and Snow are new to Super Mario Maker 2. For more variety, you can toggle each theme to its nighttime variant, which adds unique twists to the gameplay. And, of course, you can share your creations online. Super Mario Odyssey Super Mario Odyssey (for Nintendo Switch) 5.0 Outstanding In Super Mario Odyssey, the heroic plumber returns to open-world game design for the first time since the incredible Super Mario 64. Though Odyssey isn't as technically groundbreaking as its predecessor, the action-platformer is packed to the brim with hat-tossing combat. Yes, hat tossing. This time around, Mario has a new friend, Cappy, who lets Mario dispatch enemies with the flick of the wrist. And, even better, Mario can assume the identity of an enemy, gaining its abilities, by plopping Cappy on the foe's head. Super Mario RPG Super Mario RPG - Nintendo Switch (OLED Model), Nintendo Switch Lite, Nintendo Switch 4.0 Excellent Forget Paper Mario or Mario and Luigi. The original Super Mario RPG, a collaboration between Nintendo and Square Enix, first showed us that Mario’s charms could translate to a Final Fantasy-style adventure. This faithful remake offers gorgeous new graphics and increased accessibility. At last, find out who Geno is. Super Mario RPG - Nintendo Switch (OLED Model), Nintendo Switch Lite, Nintendo Switch review Super Monkey Ball Banana Mania Super Monkey Ball Banana Mania (for Nintendo Switch) 4.0 Excellent Only video games can capture the simple pleasures that come from racing monkeys inside balls. Super Monkey Ball Banana Mania remasters hundreds of classic stages from Sega’s obstacle course series in a single, cool package. Don’t let the bright colors and friendly monkey faces fool you. Rolling your monkey to the goal demands an expert understanding of the game’s unforgiving physics. If you get too frustrated, take a break with Banana Mania's wacky, multiplayer mini-games. Super Smash Bros. Ultimate Super Smash Bros. Ultimate (for Nintendo Switch) 4.5 Excellent Super Smash Bros. Ultimate has everything a fan of Nintendo’s crossover mascot fighting game could want. A faster pace better for competitive play. Every single character who has ever appeared in the series, including third-party icons such as Banjo-Kazooie, Cloud Strife, and Solid Snake. There's a new single-player mode chock-full of even more fan service. The theme song even has lyrics now.  Tactics Ogre: Reborn Tactics Ogre Reborn (for Nintendo Switch) 4.0 Excellent The original Tactics Ogre enthralled fans in 1995 thanks to its deep strategy and strong narrative. If you missed out the first time, Tactics Ogre: Reborn gives you another chance to check out this lost classic, the prelude to Final Fantasy Tactics. Just don’t expect hugely revamped graphics. Telling Lies Telling Lies (for Nintendo Switch) Her Story was a test for the kind of interactive story game developer Sam Barlow could pull off with just FMV clips and a fake computer interface. Telling Lies is the Aliens to Her Story’s Alien. Instead of just investigating one woman’s interviews, you follow four different characters. Tracing a nonlinear mystery across so many different threads can get overwhelming. Fortunately, Hollywood actors Logan Marshall-Green, Alexandra Shipp, Kerry Bishé, and Angela Sarafyan make the clips compelling watches in their own right. Besides, we’re all pretty used at communicating through video chat these days.  Triangle Strategy Triangle Strategy (for Nintendo Switch) 4.0 Excellent A tactical follow-up to the gorgeous Octopath Traveler, Triangle Strategy is a luxurious strategy role-playing game that rewards your patience. Soak in the atmosphere on the land. Become invested in the characters and political intrigue. Methodically think through every option during turn-based battles and feel like an absolute strategic genius.  Trombone Champ Trombone Champ (for Nintendo Switch) Rhythm games usually make you feel like an ultra-cool rock god. Not Trombone Champ. This zany title embraces the goofy charm of its titular instrument, delivering an experience that is both awesome and awkward. The purposefully bumbling controls make each song sound like a confused elephant putting on a concert, an effect that's multiplied in local multiplayer. A light progression system unlocks famous trombone players like baseball cards while trying to solve a sinister riddle. The game is also available on PC, but the Switch version deserves props for its hilarious motion controls that take the trombone simulation to the next level. Tokyo Mirage Sessions #FE Encore Tokyo Mirage Sessions #FE Encore (for Nintendo Switch) 3.5 Good While you wait for Persona 5 to come to the Nintendo Switch, Tokyo Mirage Sessions #FE, a late Wii U port, is the next best thing. This bewildering crossover between Fire Emblem and Shin Megami Tensei has players entering the entertainment industry of Japan’s stylish Shibuya and Harajuku districts. Of course, you also do battle against demons by summoning Fire Emblem characters through the power of song. A streamlined battle system and pop music tone should delight players who don’t even care about anime RPGs.  Unicorn Overlord 4.5 Excellent As a Vanillaware game, we’re not surprised that Unicorn Overlord has an unbelievably beautiful illustrated aesthetic. However, the game backs up its looks with deeply strategic role-playing gameplay that requires tactical thinking. Ogre Battle fans, this one’s for you. Unicorn Overlord review Void Bastards Roguelikes can be a polarizing genre as their repetitive nature, random elements, and punishing difficulty threaten to make the entire experience a waste of time. Void Bastards avoids this trap with a core gameplay loop that’s a joy to repeat and an addictive sense of progression stringing you along the whole time.Each new spaceship you raid is basically a tiny comic book-styled System Shock level with spooky enemies to shoot, machinery to hack, character traits to manage, and equipment to salvage. Use that equipment to construct permanent new weapons and perks that make you eager to start another raid. Our journey across the galaxy stretched on for hours because it’s so easy to say “just one more piece of loot.”Note that Void Bastards is published by Humble Bundle, which is owned by PCMag’s parent company, Ziff Davis. WarioWare: Get It Together WarioWare: Get It Together (for Nintendo Switch) 4.0 Excellent WarioWare is one of Nintendo’s best and most shockingly self-aware franchises. It’s about Mario’s gross, evil doppelganger starting a shady game company to get rich. Fortunately for you, these “microgames” remain a pure blast of weird and wonderful bite-sized entertainment. The new gimmick here lets you and a friend tackle challenges with different characters whose unique move sets make you rethink your approach on the fly. Hurry up! Xenoblade Chronicles X: Definitive Edition 4.0 Excellent This late-period Wii U gem finally returns to close out the Nintendo Switch era. A standalone entry of the Xenoblade saga, Xenoblade Chronicles X: Definitive Edition takes place on a lush open-world planet teeming with friendly and hostile creatures. Explore on foot or, eventually, by flying a giant mech. The dynamic RPG combat rewards smart timing and synchronizing party members. Along with improved visuals, this definitive edition adds a new epilogue story. Xenoblade Chronicles X: Definitive Edition review

1047 Games cofounder Ian Proulx took the stage at Summer Game Fest on Friday to promote his new game Splitgate 2 by calling out the current state of online shooters. Eschewing the marketing speak of most of his peers at the glossy showcase, he said he wants Titanfall 3 to come out and called his new game’s surprise battle royale mode “fucking awesome” while wearing a “Make FPS Great Again” hat. Suggested ReadingThe Week In Games: A Star Wars Classic Returns & More New Releases Share SubtitlesOffEnglishview videoSuggested ReadingThe Week In Games: A Star Wars Classic Returns & More New Releases Share SubtitlesOffEnglishSplitgate 2 is a free-to-play arena-style shooter where players deploy portals to mess with physics and the fabric of reality to outwit their opponents. “I grew up playing Halo and I’m tired of playing the same Call of Duty every year and I wish we could have Titanfall 3,” Proulx said on stage alongside host Geoff Keighley. He added that the new battle roayle mode aims to combine the old-school arena shooter sensibility with a mechanic to portal to other worlds. Out today on console and PC after a beta last month, 1047 revealed that the new mode is going live alongside the rest of the game. The subtext of Proulx’s pitch channeling President Trump’s slogan was clear: while EA cancels games and Activision leans into predictable cash-grabs, the underdog team at 1047 is shaking things up with a game by gamers for gamers. Meanwhile, the riff on “Make America Great Again” took place shortly after a clash between Los Angeles residents and law enforcement over ICE raids in the city’s garment district only blocks from where Keighley’s Summer Game Fest Play Days industry event takes place this weekend. Trump has ordered the immigration agency to arrest a record number of people every day for deportation even as ICE detention centers are criticized for overcrowding and lack of food. The original Splitgate launched in early access in 2019 and spiked in popularity. The party didn’t last, however, and by 2022, the studio abandoned the game to work on a new project. Last year it revealed that new project was actually just Splitgate 2. .

San, ni, ichi… Hajime! 🎌 Welcome to Nippon Marathon 2: Daijoubu! 🏃🍌🐶Whether you're a total newbie, or still recovering from shiba-related injuries from the OG Nippon Marathon - welcome to the weirdest marathon you'll ever run!Get ready for Nippon Marathon 2: Daijoubu, where fruit is deadly, physics are on vacation, and Shiba Inu are kawaii but absolutely relentless.🛎️ P.S. If you’re liking the sound of this so far, hit that Wishlist button—it’s a huge help for tiny teams like ours!Never Played the Original? Daijoubu! (That’s Japanese for “It’s OK!”)The original Nippon Marathon was our love letter to game show absurdity - drawing inspiration from Takeshi’s Castle (or MXC, for our American pals), Micro Machines, and slapstick Saturday morning TV.The idea was simple: 🦞 Race across Japan dodging ridiculous obstacles, 🍌 Hurl fruit at your rivals,🌀 And flail gloriously through ragdoll chaos…All while dressed as a lobster. And, it clicked: 💬 89% Very Positive on Steam 🎥 Millions of YouTube views 🇯🇵 Even got airtime on Japanese TV Fans were very excited when we announced Nippon Marathon 2, here's some of our fave reactions: What’s New in NM2? So for Nippon Marathon 2, we rebuilt everything from the ground up, building on what you love from the first game: 🍌 All-new obstacle courses with totally unexpected hazards 🧼 Ridiculous power-ups (old favourites + chaotic new ones) 🤼 The return of SoraTheTroll's iconic commentary 📺 Brand-new Create-a-Contestant mode 🕹️ And yes… online multiplayer is coming Who’s Behind the Madness? We’re Onion Soup Interactive - a married two-person indie team from the UK. We grew up glued to Takeshi’s Castle, Wacky Races, and many other completely unhinged TV show/cartoon from the 90s! Now as adults, it’s clearly hardwired into our DNA—because our mission is simple: To make unapologetically weird games that’ll have you questioning your life choices… and definitely ours. Since our debut with Nippon Marathon, we’ve been spreading joyful chaos to players around the world with our weird games.Our first Kickstarter for NM2 didn’t quite land, but we we weren’t ready anyway.So we trained in the indie dojo, unleashed the mini-game mayhem of SUPER 56, and now…We’re back. Stronger. Sillier. More Daijoubu than ever.Join the Community! We’re just two humans and a dream (and a lot of coffee), but it's our community that makes it all possible.Whether you’ve been with us since the first Nippon Marathon, discovered us through SUPER 56, or just stumbled in for Nippon Marathon 2 - we’re so glad you’re here 💛Got ideas? Fan art? Power-up suggestions? Come say hi: 💟 Discord 🐦 Twitter 📺 YouTube 🦋 BlueSky 🔗 LinkTree We post behind-the-scenes chaos, memes, dev updates, and occasionally, beta invites. Wishlist Nippon Marathon 2: Daijoubu! Hit that Wishlist button now to stay updated-and help us defeat the Steam algorithm overlords. It’s the easiest way to support the game and get notified about new updates and Shiba-fuelled madness.Thanks for joining us on this ridiculous journey.That’s Daijoubu!!!💛 Amy & Andy

This is a highly detailed beginner-friendly step-by-step tutorial on how to make animation from scratch in Cascadeur. It covers a complete process, starting with blocking all the way up to applying physics, including a thorough explanation of all the AutoPhysics filters and sliders 00:00 About this tutorial 01:06 Blocking 01:14 Import reference video 01:32 Creating first pose 01:47 AutoPosing issue 04:14 Creating second pose 05:31 About Invert Frame Indicator Hotkey Button 05:46 Creating the third pose 06:34 Creating the fourth pose 07:15 Creating the rest of the poses 08:49 Interpolation 08:54 Auto Interpolation 09:35 Setting Interpolation manually 10:20 IK and FK 12:00 Adding additional keys 14:44 Physics 15:55 Main Physics corrector 18:03 Rotation 19:44 Smooth trajectory 20:20 Smooth rotation 21:15 Compensation motion 22:09 Separation motion 23:13 Secondary motion 23:49 Snap the animation Learn more about Cascadeur license plans: https://cascadeur.com/plans Learn how to start using Cascadeur: https://cascadeur.com/learn Join our English-speaking community on Discord: https://discordapp.com/invite/Ymwjhpn Follow us on: Facebook https://www.facebook.com/CascadeurEN/ Twitter https://twitter.com/Cascadeur_soft #Animation #Tutorial #gamedev

Blender 4.5 is here, and this note comes with some impressive new features and improvements. 🌐 Explore Blender 4.5: https://www.blender.org 🔗 See More: https://developer.blender.org/docs/release_notes/ ✨ Get Premium Blender Addons: https://superhivemarket.com/?ref=110 ✨ See More Projects: https://studio.blender.org/welcome/ 🎓 Learn to Animate in Blender: https://bit.ly/3A1NWac 👨‍👩‍👧‍👦 Get Character Creator 4 - https://bit.ly/3b16Wcw 🦿 Get Iclone 8.5 - https://bit.ly/38QDfbb 🪮 FiberShop - Realtime Hair Tool: https://tinyurl.com/2hd2t5v 📂 Big Ref Database: https://bit.ly/3PLtaQ8 ---------------------------------------------------------------------------------------------------------------- ✉️ Join Weekly Newsletter: https://bit.ly/3lpfvSm ❤️Patreon: https://www.patreon.com/asknk 🔔Discord: https://discord.gg/G2kmTjUFGm 🐣Twitter: https://bit.ly/3a0tADG ---------------------------------------------------------------------------------------------------------------- █ █ Blender Premium Tutorials █ █ 🎓🥇Blender Tutorials #1: https://bit.ly/3nbfTEu 🎓🥈Blender Tutorials #2: https://tinyurl.com/yeyrkreh 🎓🔨 Learn HardSurface In Blender: https://bit.ly/3E5nP2T 🎓🚙 3D Cars Building, Rigging & Animation: https://bit.ly/4h5HXEq 🎓 🚘Cinematic Car Animation Course: https://bit.ly/3ORFccG 🎓🚴🏻 Alive! - Animation Course: https://bit.ly/3AEFvyA 🎓🧑🏻‍🎨 Human - Realistic Portrait Creation: https://bit.ly/2XvMT1j ---------------------------------------------------------------------------------------------------------------- #asknk #b3d #blender3d #free3Dresources #freetextures #freematerials #freefriday #premium #b3d #blender3d #free #addons #blenderaddons #new #3dnews #release #update 00:00 Intro 01:05 Splash 01:29 User Interface 04:57 Node Updates 06:26 Geo Node Updates 08:55 Compositor Updates 10:25 Compatibility Updates 11:14 Eevee Updates 13:00 Cycles Update 13:40 Modeling & UV Updates 14:09 Animation & Rigging 15:24 Sculpt, Light & Texture 15:57 Sequencer 16:06 Pipeline Update 16:16 Physics / Core / Python API 17:07 New Projects #SupportsArtist

Extra-sensory perception The nine-armed octopus and the oddities of the cephalopod nervous system A mix of autonomous and top-down control manage the octopus's limbs. Kenna Hughes-Castleberry – Jun 7, 2025 8:00 am | 19 Credit: Nikos Stavrinidis / 500px Credit: Nikos Stavrinidis / 500px Story text Size Small Standard Large Width * Standard Wide Links Standard Orange * Subscribers only   Learn more With their quick-change camouflage and high level of intelligence, it’s not surprising that the public and scientific experts alike are fascinated by octopuses. Their abilities to recognize faces, solve puzzles, and learn behaviors from other octopuses make these animals a captivating study. To perform these processes and others, like crawling or exploring, octopuses rely on their complex nervous system, one that has become a focus for neuroscientists. With about 500 million neurons—around the same number as dogs—octopuses’ nervous systems are the most complex of any invertebrate. But, unlike vertebrate organisms, the octopus’s nervous system is also decentralized, with around 350 million neurons, or 66 percent of it, located in its eight arms. “This means each arm is capable of independently processing sensory input, initiating movement, and even executing complex behaviors—without direct instructions from the brain,” explains Galit Pelled, a professor of Mechanical Engineering, Radiology, and Neuroscience at Michigan State University who studies octopus neuroscience. “In essence, the arms have their own ‘mini-brains.’” A decentralized nervous system is one factor that helps octopuses adapt to changes, such as injury or predation, as seen in the case of an Octopus vulgaris, or common octopus, that was observed with nine arms by researchers at the ECOBAR lab at the Institute of Marine Research in Spain between 2021 and 2022. By studying outliers like this cephalopod, researchers can gain insight into how the animal’s detailed scaffolding of nerves changes and regrows over time, uncovering more about how octopuses have evolved over millennia in our oceans. Brains, brains, and more brains Because each arm of an octopus contains its own bundle of neurons, the limbs can operate semi-independently from the central brain, enabling faster responses since signals don’t always need to travel back and forth between the brain and the arms. In fact, Pelled and her team recently discovered that “neural signals recorded in the octopus arm can predict movement type within 100 milliseconds of stimulation, without central brain involvement.” She notes that “that level of localized autonomy is unprecedented in vertebrate systems.” Though each limb moves on its own, the movements of the octopus’s body are smooth and conducted with a coordinated elegance that allows the animal to exhibit some of the broadest range of behaviors, adapting on the fly to changes in its surroundings. “That means the octopus can react quickly to its environment, especially when exploring, hunting, or defending itself,” Pelled says. “For example, one arm can grab food while another is feeling around a rock, without needing permission from the brain. This setup also makes the octopus more resilient. If one arm is injured, the others still work just fine. And because so much decision-making happens at the arms, the central brain is freed up to focus on the bigger picture—like navigating or learning new tasks.” As if each limb weren’t already buzzing with neural activity, things get even more intricate when researchers zoom in further—to the nerves within each individual sucker, a ring of muscular tissue, which octopuses use to sense and taste their surroundings. “There is a sucker ganglion, or nerve center, located in the stalk of every sucker. For some species of octopuses, that’s over a thousand ganglia,” says Cassady Olson, a graduate student at the University of Chicago who works with Cliff Ragsdale, a leading expert in octopus neuroscience. Given that each sucker has its own nerve centers—connected by a long axial nerve cord running down the limb—and each arm has hundreds of suckers, things get complicated very quickly, as researchers have historically struggled to study this peripheral nervous system, as it’s called, within the octopus’s body. “The large size of the brain makes it both really exciting to study and really challenging,” says Z. Yan Wang, an assistant professor of biology and psychology at the University of Washington. “Many of the tools available for neuroscience have to be adjusted or customized specifically for octopuses and other cephalopods because of their unique body plans.” While each limb acts independently, signals are transmitted back to the octopus’s central nervous system. The octopus’ brain sits between its eyes at the front of its mantle, or head, couched between its two optic lobes, large bean-shaped neural organs that help octopuses see the world around them. These optic lobes are just two of the over 30 lobes experts study within the animal’s centralized brain, as each lobe helps the octopus process its environment. This elaborate neural architecture is critical given the octopus’s dual role in the ecosystem as both predator and prey. Without natural defenses like a hard shell, octopuses have evolved a highly adaptable nervous system that allows them to rapidly process information and adjust as needed, helping their chances of survival. Some similarities remain While the octopus’s decentralized nervous system makes it a unique evolutionary example, it does have some structures similar to or analogous to the human nervous system. “The octopus has a central brain mass located between its eyes, and an axial nerve cord running down each arm (similar to a spinal cord),” says Wang. “The octopus has many sensory systems that we are familiar with, such as vision, touch (somatosensation), chemosensation, and gravity sensing.” Neuroscientists have homed in on these similarities to understand how these structures may have evolved across the different branches in the tree of life. As the most recent common ancestor for humans and octopuses lived around 750 million years ago, experts believe that many similarities, from similar camera-like eyes to maps of neural activities, evolved separately in a process known as convergent evolution. While these similarities shed light on evolution's independent paths, they also offer valuable insights for fields like soft robotics and regenerative medicine. Occasionally, unique individuals—like an octopus with an unexpected number of limbs—can provide even deeper clues into how this remarkable nervous system functions and adapts. Nine arms, no problem In 2021, researchers from the Institute of Marine Research in Spain used an underwater camera to follow a male Octopus vulgaris, or common octopus. On its left side, three arms were intact, while the others were reduced to uneven, stumpy lengths, sharply bitten off at varying points. Although the researchers didn’t witness the injury itself, they observed that the front right arm—known as R1—was regenerating unusually, splitting into two separate limbs and giving the octopus a total of nine arms. “In this individual, we believe this condition was a result of abnormal regeneration [a genetic mutation] after an encounter with a predator,” explains Sam Soule, one of the researchers and the first author on the corresponding paper recently published in Animals. The researchers named the octopus Salvador due to its bifurcated arm coiling up on itself like the two upturned ends of Salvador Dali’s moustache. For two years, the team studied the cephalopod’s behavior and found that it used its bifurcated arm less when doing “riskier” movements such as exploring or grabbing food, which would force the animal to stretch its arm out and expose it to further injury. “One of the conclusions of our research is that the octopus likely retains a long-term memory of the original injury, as it tends to use the bifurcated arms for less risky tasks compared to the others,” elaborates Jorge Hernández Urcera, a lead author of the study. “This idea of lasting memory brought to mind Dalí’s famous painting The Persistence of Memory, which ultimately became the title of the paper we published on monitoring this particular octopus.” While the octopus acted more protective of its extra limb, its nervous system had adapted to using the extra appendage, as the octopus was observed, after some time recovering from its injuries, using its ninth arm for probing its environment. “That nine-armed octopus is a perfect example of just how adaptable these animals are,” Pelled adds. “Most animals would struggle with an unusual body part, but not the octopus. In this case, the octopus had a bifurcated (split) arm and still used it effectively, just like any other arm. That tells us the nervous system didn’t treat it as a mistake—it figured out how to make it work.” Kenna Hughes-Castleberry is the science communicator at JILA (a joint physics research institute between the National Institute of Standards and Technology and the University of Colorado Boulder) and a freelance science journalist. Her main writing focuses are quantum physics, quantum technology, deep technology, social media, and the diversity of people in these fields, particularly women and people from minority ethnic and racial groups. Follow her on LinkedIn or visit her website. 19 Comments

Scientists have discovered that under the right conditions, a gummy bear-like ball can roll down a vertical wall all by itself—upending a core assumption in physics.

Simulations suggest where we might look for the mystery material.

Get the latest and greatest iPhone 16 Pro Max for free when you open a new Unlimited Ultimate line with Verizon. Here's how to do it.