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zetric-plains · 1 year

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Some very extravagant marking examples below

OUR SPECIES IS FULLY OPEN SO MAKE WHATEVER TRAITS YOU WANT

Some Zetrics have floppy ears, most have upright.

The more wild a Zetric Dragon is the more dragon-shaped its face and eyes will be. (Sample below)

A lot of Zetrics interact with humans and thus developed a more friendly appearance. Wild Zetrics aren't exactly fond of humanity but usually won't attack them unless threatened. (They sometimes form groups to hunt and the lead will stand taller and walk with a stride that screams confidence. They often act this way interacting with domestic Zetrics.)

Wild and Domestic Zetrics breeding does not count as hybrids. Their differences are very little after all and much more limited to shape and behavior.

A key way to tell is the flatter heads of the wild zetrics, sharper eyes (often with little to no whites showing, nostrils closer to the end of the snout and a more defined jaw. Pups are a bit bulkier than domestic pups

This is our skeletal structure

Uncommon Zetrics (below) might have coloring on one spade that isn't on the other spades. Whether it's a tail or an antennae spade. But the spade color stays exactly the same as long as it doesn't disappear in a same-colored marking. A few can be born every 1-4 years.

Extremely rare Zetrics (below) may also have the same marking be a completely different color! Like this! (These dragons often succeed the most in cometitions because they're extremely confusing for others to look at and they don't know which "eye" to concentrate on)

These only happen on two different colored antennae/a different colored tail. Even rarer occurances have three different eye colored markings, but they're only born once every millinia. These occur once or twice every Zetric lifetime. (about every 300-500 years)

This is a hybrid of a winged dragon and a Zetric. Hybrids CANNOT reproduce. (<The Zevolx were a very rare exception to this rule.) The Zetrics can reproduce with anything but their offspring are always sterile

(below image) These split tail/head mutations may also be a result of deformity but sometimes, they can be one egg absorbing another in the womb. But instead of splitting fully down half and half, one dominates and the color markings of the dominating one stay throughout the body. (Mutations DO NOT count as hybrids)

Base you may edit

AND FINALLY COLOR TRAITS

Zetrics can have extravagant colors and patterns.

stripes/bands, spots, socks and blotches are the most common markings.

Blotches are far more likely to result in multi-colored paw pads and claws than any other kind of marking. But they are not rare or uncommon to any form of marking.

piebalds with stripes and calicos are less common

piebalds with spots and rosettes are very uncommon but not rare.

Albinos and melinistic Zetrics are rare but do exist. Their eye markings and other markings often very faded versions of what they would be. But still faintly existent.

likelihood of options with offspring. (roughly by 5s)

underbelly - 50%

mostly single colored 20%

Stripes/bands - around an 80% chance of passing

Spots - around a 75% chance

Socks 85% (can really appear with any of the other markings or no other markings)

Blotches 30-50% chance (more recessive when it comes to breeding with stripes, spots and sock markings but often go hand in hand with socks)

striped piebalds 20-25% (more likely if bred with blotched with a history of striped parents)

Calico 15-20% (more likely with two blotched parents)

spotted piebald 10%

rosettes (more dominant over piebalds and calicos but still fairly rare and recessive to more dominant genes) 10-25%

Albino/Melinistic 1-2% (often still have faint markings underneath)

you can ignore this, have fun.

IMPORTANT: Zetric Dragons can change their fur colors for a temporary time so they may hunt! The only thing that doesn't change are their "eyes", Claws and of course their actual eyes

#zetric info #make an oc

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grailfinders · 3 years

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Fate and Phantasms #197

Today on Fate and Phantasms we're getting festive with Attila the San(ta)! We do dip into Fighter just a bit, but that's because she's got a candy cane that can turn into pretty much everything, so you gotta be prepared. She's mostly a Swords Bard to channel Dumuzid's whimsical story of Santa Claus into the aforementioned Candy Cane of the War God, as well as a Divine Soul Sorcerer. Some things don't change.

Check out her build breakdown below the cut, or her character sheet over here!

Next up: Something something Super Mario 64, something something Dark Souls

Race and Background

I know last time we made Altera a human, but I think we're going to change up her race between versions for once. Less because she is a different race, more because time marches on. Altera isn't quite human, so this time around she'll be a Custom Lineage. That gives her +2 Dexterity, as well as Performance proficiency to really nail those ho ho hos. You might be santa, but you also get a gift for starting with this race; the Gift of the Chromatic Dragon, that is! Once per long rest, you can add 1d4 of elemental damage to a weapon's damage rolls for a minute as a bonus action. Look, one of the things the candy cane can turn into is a whip, and it needs all the help it can get being useful. Also, proficiency times per long rest you can use your reaction to gain resistance to one instance of elemental damage. Her Natural Body might be a bit weakened by her cold, but it's still there.

She's also still an Outlander, giving you proficiency with Athletics and Survival.

Ability Scores

First up; Charisma. You need it to give gifts to good little boys and girls, and your magic comes from your own soul, pure as fresh snow. Second is Dexterity, because you don't wear armor and you need it for your whip. It'll also make you better with that bow and arrow, the key of any archer! Your Strength is also pretty good, we won't be focusing on it, but you are still beating people to death with a cane, so it can't be low. Your Constitution is above average, if lower than usual thanks to your illness. That means your Intelligence is low, and your Wisdom is lowest. It's hard to think or smell when you've got a cold. Better luck next year.

Class Levels

Fighter 1: Yup, starting off with the one level dip. This gets you all the weapons you could want, and you get a little more HP, super important at level 1. Starting here gets you proficiency with Strength and Constitution saves, as well as the Intimidation skill -you're still the leader of the huns, after all- and Animal Handling. You also get a Second Wind as a bonus action once per short rest to drink a cup of hot cocoa and heal up. How nice. Finally, pick up a Fighting Style. Archery will be super helpful for an archer class servant, giving you +2 to weapon attack rolls made with a ranged weapon. What do you mean she throws sheep.

Bard 1: Now that we've got all we want from fighter, let's hop over to the star of the show, Bard! I'll put that one skill proficiency in Religion, you get your normal and seasonal powers from different gods, make sure you don't mix them up. Anyway, you get Bardic Inspiration, giving an ally a d6 as a bonus action Charisma Modifier times per long rest. They can then use this d6 to add the roll to any one attack, check, or save. For more fun, you get Spells that you cast using your Charisma. Grab Blade Ward so you can still be a pseudo-barbarian, and Dancing Lights to spread some christmas cheer. You also get Animal Friendship to herd sheep more easily, Disguise Self for the perfect Elder Claus stache, and Heroism to make your allies a bit bolder this holiday season. Also, it's more like Dumuzid is casting Speak with Humans, but you casting Speak With Animals is slightly more reasonable.

Bard 2: Second level bards are a Jack of All Trades, adding half their proficiency bonus to skills they aren't proficient with. This means you've got zero negative skills now- I guess it wasn't much of a cold after all. You also get a Song of Rest for more healing over short rests, but I'm not entirely sure how that works in character. You learn Color Spray this level. I'm not sure blinding people is mechanically something you do, but at least it looks the part.

Bard 3: Third level bards graduate from college, and the college of Swords is great when you need to use a whip and mean it. You get another Fighting Style, so pick up Dueling this time for a +2 bonus to one-handed weapon damage. You also get Blade Flourishes, spending a die of bardic inspiration once per attack action to deal extra damage, move an extra 10 feet, and add effects to an attack. A Defensive Flourish add the amount rolled froma bardic inspiration die to both the damage dealt and your AC for the rest of the round. A Slashing Flourish lets you do a little ribbon dance with your whip, dealing the amount rolled to a second creature as well. A Mobile Flourish launches the creature back, dealing the roll in damage and pushing them 5 feet plus the number rolled. Put a little Christmas magic on your cane to shake up how you hit people, easy. You also get Expertise in two skills, doubling your proficiency with them. Double down on Religion and Animal Handling to get a better handle of your new powers and your mount. You can cast Enhance Ability to make everything you do a little better. Well, not everything, you have to pick one type of ability score check per casting, but still, potentially everything.

Bard 4: Fourth level bards get your first Ability Score Improvement. We need to round up your charisma anyway, so grab the Resilient feat to do just that and get proficiency with charisma saves. You can't banish Santa, he'll just come down the chimney again. Also, grab Prestidigitation to make presents out of nothing, and Knock to get into people's homes. It's a bit noisy, but I doubt someone half-loopy from illness will be a master thief.

Bard 5: Fifth level bards get a better inspiration die, launching d8s instead of d6s. They also become a Font of Inspiration, so you get dice back on short rests instead of long ones. You can also put on Motivational Speeches to rally your party around the one true meaning of Christmas: destroying bad civ.

Sorcerer 1: Bouncing over to Divine Soul sorcerer gives you the best spell list in the game, mostly because it's two spell lists. Cast 'em with your Charisma, check the multiclassing section to figure out how many slots you have. Grab Green-Flame Blade for an extra shiny candy cane, Lightning Lure to use said candy cane to drag people towards you, and Guidance and Resistance to be better than most people. You hang out with a god now, this kind of thing will happen. You also get Mage Armor so you can finally get out of that stuffy leather coat, as well as Shield of Faith for even more AC. You also get an extra spell that is supposed to be based on your alignment, but screw that, grab Inflict Wounds for a really scary candy cane whapping. On top of all that, you are Favored by the Gods, meaning you can add 2d4 to a failed save or attack once per short rest.

Bard 6: Sixth level bards get Countercharm, letting you spend an action to give advantage to nearby allies who are making saves against being charmed or frightened. But that's bad, just attack twice thanks to your Extra Attack. You also learn Tongues, because you can't deliver toys all over the world if you can't understand toy commercials all over the world.

Sorcerer 2: Second level sorcerers become a Font of Magic, giving you your sorcerer level in sorcery points per long rest. You can get more (up to your sorcerer level) by burning spell slots, or vice-versa. You also learn how to cast Magic Missile, for some caster... archer... balls. Whatever. Hit people with magic.

Sorcerer 3: Third level sorcerers learn Metamagic, letting you control your magic a little more than most servants. Transmuted Spell lets you change a spell's damage type, so now your weapon replacement spells can deal the same types of damage. You also get a Heightened Spell, letting you force disadvantage on one person affected by the spell's saving throw. If you throw enough sheep, one of them will hit eventually. Speaking of spells, you get Scorching Ray, letting you send an array of flaming hot sheep at your enemies, making an attack roll for each sheep.

Sorcerer 4: Your last level of sorcerer gets you another ASI. Bump up your Charisma for more powerful sheep-based attacks. Speaking of, you learn Melf's Minute Meteors, creating six tiny sheep that follow you around. When you cast the spell, and each bonus action thereafter, you can throw 1-2 sheep at a point within 120', where they then explode. Every creature within 5' makes a dex save, and they take damage if they fail or half if they succeed. A bit more brutal to the sheep, but you can't argue with results.

Bard 7: Seventh level bards get fourth level spells like Dimension Door. You gotta end up in the sky somehow for your NP.

Bard 8: Eighth level bards get yet another ASI, so bump up that Dexterity. There really aren't any other spells I want for this build at fourth level, but take Freedom of Movement anyway. It should probably be a lot harder to break into the underworld than you make it look.

Bard 9: Ninth level bards get fifth level spells, and their song of rest gets a bit stronger, turning into an extra d8 of healing. Grab Awaken to turn a regular sheep into a cool, smart sheep. Unfortunately, sheep are small creatures, so you won't have a mount, even if you use the Custom Lineage to make a mini-santa. If you want to keep with the theme you could always get a cow, I guess. No matter what you awaken though, it's charmed by you for up to 30 days, after which it'll do whatever it feels is best. Be nice to Dumuzid.

Bard 10: Tenth level bards get a lot of stuff; Expertise in performance and athletics to be the fittest goddamn Santa alive, the Light cantrip for more Christmas decorations, a boosted Bardic Inspiration die, and best of all, Magical Secrets. That last one gives you two spells from any spell list, as long as they're at a level a 10th level bard could cast. Grab the Shillelagh cantrip to make your candy cane stronger without having to invest in strength, and Conjure Woodland Beings to create some real sheep. Probably not the best use of a 4th level spell slot, but why not. Eight sheep.

Bard 11: Eleventh level bards get sixth level spells, and now you can finally set up for the christmas party with a Heroes' Feast. More HP, advantage on wisdom saves, and anyone who partakes can't be frightened, that's some good mood food.

Bard 12: Use your last ASI for the Tough feat, giving you +2 HP for each level you have. We have to keep your constitution low because of your cold, but you're still Attila the Hun, you should be pretty tough to fight.

Bard 13: Seventh level spell time! Grab Prismatic Spray to launch a whole herd of rainbow-powered sheep in a 60 foot cone, forcing a dexterity save on every creature inside it. They then get hit by one of eight colored beams, dealing plenty of damage, petrifying them, or banishing them, all depending on the sheep that hits them.

Bard 14: Time for your final sword bard goodies! As a proper swordsmaster, you get a Master's Flourish, letting you use your flourishes freely, but restricting the damage to a d6 when not burning inspiration. The cane's pretty flowy, so restricting it just doesn't make sense. You also get another round of Magical Secrets- this time you can Conjure Fey to finally make a proper big Dumuzid to ride, and cast Haste to boost yourself now for a drawback later, just like your third skill. For Dumuzid, I assume an "Awakened White Moose" from Icewind Dale should work, but I don't have that book to confirm it.

Bard 15: Your capstone level is another boost to your bardic inspiration for the most damage and support possible, a d12. You also get one last spell, this time at eighth level, Mind Blank. You are made immune to psychic damage and can't have your mind read for 24 hours, and it's even powerful enough to shut down the Wish spell. You can't read a mind that isn't thinking about anything.

Pros and Cons

Pros:

For someone using a whip sometimes, you do pretty good damage. Gift of the Chromatic Dragon will probably last an entire fight, and without concentration it's just free damage. Tack on your flourishes and haste, and you're dealing 6d4 + 2d12 + 18 damage per turn- with median rolls, that's almost 50 damage, and you can keep that up for a couple rounds easily.

You also come packing with a lot of variety in your spell list, with plenty of damage and utility to help you in and out of combat.

Speaking of out of combat, you're weirdly good with skills. Jack of all trades mean you'll never have a negative modifier on a skill check, and Favored by the Gods and Enhance Ability push your advantage as far as it will go.

Cons:

Playing to character means you're using a lot of fire damage, the most easily resisted in the game. Ironically you're going to fight Ereshkigal, so not getting radiant damage is actually helping you a lot. But that doesn't change the fact that fire is the most resisted type.

A lot of your early build doesn't focus on damage at all, so it'll be hard to keep up with the rest of your party in big fights for a while.

Playing to character is a bad idea. We talked about fire already, but also- summoning sheep is a terrible use of a spell slot. Awakening a sheep is a terrible use of a spell slot. Using a whip is just bad, period. Please, feel free to shake things up before bringing it to a tabletop game.

#fgo #fate grand order #D&D 5e #DND #Attila the san(ta)#bard #fighter #sorcerer

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popchoc · 2 years

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its very obvious that Maya is your favorite so obviously you're going to take her side in everything but i'm confused why you give her character a pass in this whole disaster of a storyline and will still ship her with other characters because the couple is ruined but you seem to just hate carina as a character now? both characters have been ruined with this whole thing. i mean if you're not going to watch anymore it doesn't matter but its just weird

I've never claimed that Maya isn't my favorite. She is, and she's allowed to be. There's nothing wrong with liking one character more than another. I have liked Carina for a long time though, especially in her first season of Grey's and also at her start of Station 19. They just took the things I enjoyed about her about 10 notches too far, which resulted in, yes, almost hating her. She went from funny assertive to pushy to bossy and toxic, and that's not something I find entertaining. I can't see why Maya needs some blame too, except for letting it all happen. That's what's ruining her. And that's what saddens me, and not just because it makes me miss the season 1 and 2 version of her.

I never said I'm not watching anymore, I'm just not making it a priority which isn't just because of them. I never watched for just them, plus my annoyance about them goes way beyond the baby and/or Jack story. I've always shipped Maya with pretty much everyone (let's face it, she's very shipable - lol). And when things were different I could think the same about Carina. But when it comes to it, things aren't the same here. Unlike with Maya, who's been around since the start and really fits in, they already have difficulties writing Carina involved with one of them; I can't imagine what they'd do with her without such involvement, so I'm sorry to say this, but that sounds like "back to Grey's" to me. And that's why, regarding to this show, yes, it will always be Maya over Carina to me. I just really, really wished I'd never had to come to that conclusion. And that, my friend, is the writers fault, and no one else's.

#ask #station 19

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ramajmedia · 5 years

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10 Of The Most Iconic Jim Henson Creatures (That Aren't Muppets), Ranked

Most of us are familiar with the genius of Jim Henson, whether from The Muppets, Sesame Street, or any number of his films. The famous puppeteer and creator certainly had a gift for creating memorable and visually stunning characters. So much so, in fact, that an entire workshop was created dedicated to the production of some of these famous creatures.

Classic shows like The Storyteller and Fraggle Rock (and movies like Labyrinth and The Dark Crystal) owe everything to this visionary. Some of their most wonderful creations were all conceived in Jim Henson's Creature Shop. Today, we're having a creature feature as we spend some time with ten of the Jim Henson Company's greatest creature creations. Oh, and don't worry: as you can see, we haven't forgotten the Muppets; they've been ranked separately!

10 Bear in the Big Blue House

We'll start our list with a howdy from the big bear himself, Bear from Bear in the Big Blue House. One of the largest creatures created by Henson's company (along with characters like Sweetums), Bear was the warm and inviting star of his own show. It aired on the Disney Channel in the 90s.

In the mornings, Bear would welcome viewers into the titular Big Blue House for a day with all his friends, such as Treelo, Ocho, Pip and Pop Otter, Shadow, and Luna the Moon. Bear was as big and warm as his personality, and he always made his viewers feel welcome. What better way to start out our list?

9 Rankle, Rose, and Edgar

What do a reanimated cat mummy, a zombie raccoon, and a werewolf with a sweet tooth have in common? They are all friends of the quirky and charming Christine McConnell. These three are certainly some of the more adult characters the company has created, but at the same time, they are as charming as any Muppet or other creation.

RELATED: Sesame Street: 10 Best Celebrity Guest Stars Of The Last 50 Years, Ranked

Brought to us by Henson Alternative, Rankle, Rose, and Edgar are easily the highlights of the show. Rankle is snarky, sarcastic, and mildly sinister, Rose is bawdy and loud, and Edgar is a teddy bear with a horror-movie-quality exterior. What's not to love?

8 The Sinclair Family

Created in memory of the famous Muppet-maker, Dinosaurs was a sitcom that centered around the prehistoric happenings of the Sinclair family. For four seasons, viewers tuned in to the lives of Earl, Fran, Robbie, Charlene, and their hatchling, Baby Sinclair. The show was a weird but wonderful combination of creatures and comedy that had quite the following.

Despite its use of creatures, the sitcom jumped through all the genre hoops in the way of Family Matters, Full House, and Boy Meets World. It had the family-centric narrative, but also tackled some interesting issues, including a controversial season finale. It was a strange show, but certainly one we can appreciate.

7 Gelflings (2019 Version)

The Dark Crystal is arguably one of Jim Henson's greatest creations; essentially his Lord of the Rings. As much as we wanted to include Jen and Kira from the original film, the prize has to go to the newer Gelflings featured in the new Netflix series.

The Gelflings, as their name might allude, are elf-like creatures from the land of Thra. In Age of Resistance, there are even tribes of them somewhat akin to the elves of Tolkien. Rian, Brea, and Deet are three of the new Gelflings, and they could not look better. They have better puppet models, a more high-fantasy design, and their different personae are absolutely enchanting. Color us impressed.

6 Skeksis

On the other end of the Dark Crystal spectrum, we have the sinister and insidious Skeksis. This breed of nightmare fuel is quite possibly the most horrifying thing Henson ever dreamed up. With their beaks, claws, teeth, and aristocratic sense of style, there's definitely something outright evil about their persona.

From the snarling Emporer Skeksi to the creepily charming Chamberlain, the Skeksis have ruled Thra with an iron claw, bewitching and deceiving their world to their whims. They are truly as hideous on the outside as they are within, but we still love watching them. They're easily one of our favorite monsters.

5 Creatures of the Labyrinth

Though we have a soft spot for Sir Didymus, we couldn't pick just one creature for this spot. For those who haven't seen this marvelously magical film, Labyrinth is Jim Henson's collaboration with the legendary David Bowie, which resulted in one of the most iconic fantasy films of the 80s.

RELATED: 10 Things You Didn't Know About Labyrinth

Jareth, Hoggle, Ludo, and all the legions of monsters that inhabit this mystical magical world were just too many to count. Worthy of a list all their own, the creatures from the titular labyrinth could rival those of Dark Crystal fame, but we'd be lying if we said Bowie didn't give them an unfair advantage.

4 The Fraggles

Dance your cares away and let the music play, down in Fraggle Rock with these colorful creatures. The Fraggles are small, carefree critters who, along with the workaholic Doozers, live their lives and go on adventures in the caves of Fraggle Rock.

RELATED: 10 Most Underrated Jim Henson Creations

Gobo, Mokey, Wembley, Boober, and Red are just the starring cast of Fraggle Rock, but there are legions more of the fuzzy creatures living beneath the home of Doc and his dog, Sprocket. These lovable creatures are some of Jim Henson's most memorable characters, and we can see why. Much more than Muppets, the Fraggles delighted kids for five seasons and 96 episodes.

3 Aughra

Frank Oz couldn't have put it better any other way: she's so ugly she's beautiful. Yes, we've mentioned the rest of the Dark Crystal characters already, but we can't leave out Aughra. Aughra is one of the most powerful beings in the realm of Thra, as well as one of the most uniquely-designed creatures the Creature Shop has ever created.

Born from the rocks before even the race of Gelflings, Aughra is the only one of her kind. She's a mystic, a wizard, and a cosmic being all rolled into one. As one of the most strange and mystifying creatures on our list, you can bet we applauded her return in Age of Resistance.

2 Teenage Mutant Ninja Turtles

Bringing Leonardo, Donatello, Raphael, and Michaelangelo to the big screen outside of animation was no easy feat. Enter Jim Henson's Creature Shop to bring them to life. Using a mix of puppetry and full-body effects, the turtles sprang from the sewers and onto the big screen for the very first time.

Though the characters themselves were not created by Henson or his crew, the technology to bring them to life was. This led to the creation of the Henson Performance Control System, which revolutionized puppeteering and practical effects. If it wasn't for this film, who knows where the creature shop would be.

1 Big Bird

Arguably the most famous resident of Sesame Street, Big Bird has entertained legions of children and even adults since he first appeared in 1969. The large yellow avian has represented every curious child to ever tune in to the popular PBS program, teaching them the value of imagination and an appetite for learning.

From his bright, yellow, fluffy exterior to his enormous heart, Big Bird has delighted millions of viewers the world over. Though not a product of the Creature Shop, without Big Bird there might not even be a Sesame Street. Adorable, curious, and even a trendsetter, how could we not give the big guy our number one spot?

NEXT: Sesame Street: 10 Hilarious (And Adorable) Bert And Ernie Memes

source https://screenrant.com/jim-henson-most-iconic-creatures-besides-muppets/

#screenrant

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mustafakemalpasha · 7 years

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Playing with Balls

Let me start with the simplest case of gravity balls so that you can really get a feeling for what's going on. Suppose I have two balls somewhere in space. It's just these two balls and nothing else — no planets, no stars, no Starbucks nearby. In that case the only interaction between the two balls would be gravitational. What will happen to these two balls? Since there is a gravitational force pulling them together, they will both increase in speed (that's what forces do). But as they move closer together, the gravitational force increases even more. Overall, it's an interesting motion problem.

This gravitational force would depend on the product of the mass and the distance between the two balls.

These two balls are somewhere with respect to some origin (it doesn't really matter). What matters is the vector from A to B which we can label as just r. With this vector r, I can find the gravitational force on ball B as:

I should point out a few things with this expression. This is the gravitational force on B as exerted by A. There is also a force from B on A, it would have the same magnitude but opposite direction. The G is the universal gravitational constant. The r with the "hat" is called r-hat (surprise) and it is a unit vector. This unit vector doesn't change the magnitude of the force, but without it, you would just have a scalar force and that wouldn't be so useful.

What do we do with the force anyway? The gravitational force on object B can be used to find the change in momentum of B after some time interval where the momentum is the product of mass and velocity. This comes straight from the momentum-principle.

Yes, the p is momentum. Before you ask, I don't know why we always use "p" for momentum. I guess it's because "m" was already taken to be used for the mass. OK, there is one more equation. If I know the object's momentum, then I can use the definition of momentum and average velocity to find the new position of this thing after some short time interval.

The r-vector represents the position since "p" was already taken. That was just a joke: Actually, we use "r" for position because it comes from the "r" in spherical coordinates. But this leads to something good. It goes like this: calculate the force, update the momentum and then update the position for some short time interval. Do this also for the other mass. Since the positions change, the force changes so you need to do it all again. And again. And again. Keep doing this until you want to stop — and boom. That's the whole idea behind a numerical calculation.

Let's just do it. Here is a numerical calculation for two masses in space. Go ahead and click the "play" to run and you can see the code by pressing the "pencil" icon.

I tried to put some comments (comments are lines with the # symbol in front of them) in the code so that you can sort of figure out what is going on if you want to play with it. It might not look like anything is happening at first because the balls start off really slowly. Just wait and you should see something.

What happens to the balls? They do indeed start to move towards each other and speed up during that process. However, they aren't real balls so that there is nothing preventing them from passing through each other — and so they do. After that, the gravitational force slows them down until they start moving towards each other again. If you let it, these would just oscillate back and forth forever.

Also, I cheated. The balls have a mass of 1 kilogram, but I changed the universal gravitational constant to some much larger number than the real life version. In real life these balls would take forever to get together since real gravity is super weak.

Finally, one other note. If you look at the code you can see that when the balls overlap, I set the gravitational force to the zero vector. There is a reason for this — it's not just because I'm crazy. If the center of the balls get really, really close then the magnitude of the r-vector is really, really small. A small r means a giant gravitational force. This giant gravitational force for a very short time can make weird things happen. The overlap force of zero prevents weird things.

More Gravity Balls

OK, but I think we can agree that two interacting gravity balls are sort of boring. What about 10 gravity balls? How would you make 10 balls interact? It's really just more of the same thing that worked for just two balls. With 10 balls, I can take one ball at a time. I need to find the distance to all the other balls and the gravitational force from all other balls. After that, I can update the momentum and position for that ball. Oh, I still need to do the same thing for the other nine balls. Yes, it's a bunch of work — but that's why I'm making a computer do it instead of me.

Here is an animation of what this looks like. If you want to play with the code (and you should), it's right here.

That's pretty cool right? Notice that I gave the balls a random color — just for fun. Also, these things will just keep moving around forever (or as long as the program runs). But what's next? How about 100 balls! No wait, 200 balls! This is the exact same code as before, just with more gravity balls. Actually, this is running at 5x speed so that it goes faster.

I don't know about you, but I'm really starting to get excited. You really need to check out the code and run it yourself (you can't break anything — I promise). See how many gravity balls you can run before your computer explodes (no, it won't really explode). Of course as you increase N (the number of gravity balls) you dramatically increase the number of computations. Not only do you have more balls to update with the momentum, but each ball has more balls that exert a force on it. I can get up to 1,000 balls, but it doesn't run super-fast.

Adding a Drag Force

Let's change it again. I don't want these balls to oscillate in and out forever. I want them to settle down into one big blob. I can do that by adding a drag force. This drag force has two main properties. First, it has to be in the opposite direction of each ball's momentum (or velocity) so that it makes the ball slow down. Second, the drag force should be proportional to the magnitude of the momentum so that a ball at rest has no drag force and a super-fast ball has a super high drag force.

Actually, I've had a drag force in the code the whole time — but the drag coefficient was set to zero so that it wouldn't do anything. If I put the coefficient to some arbitrary value (I picked 0.2), this is what happens (for 100 gravity balls). Note: I increased the playback speed by a factor of 10 — just because I wanted to try it.

If you zoom in to the final form, it looks like this:

The individual gravity balls still move around a little bit. Most of the balls are within the radius of the other balls (they are overlapping) so that most of these do not have a gravitational force on them. For the ones that do have a gravitational force, they get pulled back into the ball blob.

A Different Random Distribution

After playing with the gravity balls for a while (I hope someone is keeping track of how many times I write "gravity balls"), I saw something weird. With a large number of balls, I always get a formation that looks like this.

Hopefully you can see that "x". Why is there an "x"? Actually, you can even rotate this distribution of balls around and it's still and "x" in three dimensions. I think I know the cause of the "x". I created 1,000 gravity balls by picking three random numbers for each ball position. The x, y, z coordinates of each random number is between -1 and 1 so the possible positions of balls would be a “2 x 2 x 2” cube. Of course, the average center of mass for a distribution would be in the center of this cube and the masses are all attracted towards that point. But the non-spherical distribution of balls must be the cause of this x-feature.

I can test this supposition if I make a spherical distribution of gravity balls. Instead of creating random x, y, z coordinates, I am going to use spherical coordinates and create the following three variables: r (0 to 1), θ (0 to π), and φ(0 to 2π). This should make a spherical distribution and there shouldn't be the resulting "x" pattern. Here we go.

Looks good. Oh, since this distribution has 1,000 gravity balls, I will play it back at 30x speed.

Extension

There are many questions you could answer for this situation.

• In this gravity balls model there is no force when two balls overlap. How can you make this interaction so that it is more like “hard” sphere collisions with no overlapping?

• Is energy conserved in the case of 100 gravity balls with no drag force? What about momentum? Making a graph would help make the determination.

• Do you get significantly different results if the ball masses are not constant? Give the balls a random mass within some random range.

• I don't know if this will work, but what would happen if a giant collection of gravity balls (let's say 500) had a slight rotation to begin with. When the whole thing compresses into a compact ball, would that ball be spinning super-fast? It should. Oh, don't forget about the drag. If your drag force is too high you will lose angular momentum.

• What if you just give all the gravity balls some small random momentum to start with. What happens then?

• Suppose there were two massive gravity balls at the edge of the distribution of balls (opposite ends). Could these two balls make two different blobs form? That would be cool.

• Well, how does it feel to play around with your balls? Did you try playing around with the drag coefficient? You should.

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