#Dragon curve

[lesbianslovebts]

For this project, I took a stage 9 dragon curve and implemented the following rule: for each of the stage 8 fractals contained within the stage 9 fractal, where 4 lines enclose a square, there is 1 bead. I made the background black and then assigned a color to each column. The rainbow is because I am gay, of course. :]

#my aesthetic is gay math dragon btw #fractal #fractals #fractal geometry #dragon curve #dragon #dragons #mathematics #math #math art #beading #llbtsart #llbtspost

[blake447]

Strange way of drawing the Dragon Curve

Alright, so real quick I just want to share potentially the most arcane method of drawing the Dragon Curve I've ever seen, derived and designed by yours truly! As far as I know, this is a novel solution. I know the sequence it generates is known, but I'm not sure if anyone else has used this method before. Its quite elegant if I may say so myself.

So for those that aren't aware in programming the "<<" and ">>" operators are sometimes known as "bit shifts." Basically what this is doing is starting at some number, adding a power of two, then getting a specific 1 or 0 in the binary representation of that number iteratively, until its searched enough bits to know they aren't going to change anymore.

It has to do with this sequence right here. I've mentioned before, my personal favorite way of generating the dragon curve is to start with the sequence 0, reverse it, add one, roll over once you reach 4, and tack that on to the original sequence. So 0 0 1 0 1 2 1 0 1 2 1 2 3 2 1 0 1 2 1 2 3 2 1 2 3 0 3 2 3 2 1 Well what ends up happening is each time you add one, its like adding one to the reversed part of the newly added sequence. So we can track where all these 1's come from based on when they're added. For example, the 1 we added in the "01" step turns into 0 1 0 1 1 0 0 1 1 0 0 1 1 0 Note from here on out its palindromic, so reversing it no longer has any effect. What we end up with is a repeating pattern of two 1's, then two 0's, starting with half that many 0's. When going from 0 1 0 1 2 1 We're adding 1's to the entire second half, so in this step the 1's propagate to 0 0 1 1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 And again, this is now palindromic. Four 1's, four 0's led by half that many. One of the things I've learned about the dragon curve is just how intrinsically linked it is to binary (and this makes sense when you think of the folding paper method of generating it. Here's an excel spreadsheet demonstrating this in action

Now here's the fun part. My research was to parallelize this algorithm. One approach is to say "Okay, how can we calculate each term in this sequence without looking at the previous ones." And the answer is to exploit these very predictable patterns. And how do we predict these patterns? Simple, we simply count in binary

The right most column is useless, but starting at the next one to the left, we see a familiar pattern, almost. Say we want to know what the 5th number in the dragon curve sequence is (0 indexed). To make the sequence only lead with one 0 instead of two, we need to offset by 1, then all we have to do is increase the number by (n + 1) = 5 and take its 2nd least significant bit (1 indexed because english). The 2nd bit of ( 1 + 5 = 6 ) is a 1. For the next iteration we're looking at the 3rd least significant bit. Here we need to offset by 2, and then we increase the number by 5 again and the 3rd significant bit is the one we take. The 3rd bit of (2 + 5 = 7) is another 1 After that we're looking at the 4th least significant bit. We need to offset by 4, then increase the number by 5, and the 4th significant bit will give us our number. The 4th bit of (4 + 5 = 9) is going to be another 1, bringing our total to 3. Here's a visual representation

This is where the "1 << i" comes in, because that's the same as saying 2^i, which is how we get those offsets of 1, 2, 4, then 8, 16, 32... the "n" in "n + (1 << i)" comes from us offsetting to get the nth term in each sequence Finally the " >> (i + 1) " and "% 2" are to fetch the (i + 1)th bit from the number. After that the increasing size of the leading zero's outpaces our constant offset of the number 5, so we are only going to get 0's from here on out, and we can actually stop, hence the usage of bit length to terminate the loop early.

And if we look at the the 5th element of the sequence (0 indexed) 0 1 2 1 2 3 Funnily enough, in python this brings an actual speed increase (or at least, distributes the cost over the drawing) because of how slow reading and writing to memory is, compared to how math and bit-wise operations are implemented in low level C behind the scenes. Additionally, since there is no reliance on previous work this task can be multi-threaded, or even GPU accelerated if need be. Finally, if you've made it this far, here are a few images of some close ups of dragon curves from my GPU implemented (unrelated to this one entirely) just so that there's something pretty. Enjoy <3

#Dragon curve #fractal #programming #progblr #codeblr #python #fractals #math #computer science #algorithms #binary

[technician-the]

#fractal #fractal art #dragon curve

[vacuously-true]

your posts about dragon curves gave me vivid recollections of being a small child folding a strip of paper in half twice, seeing a level 2 curve without realizing it. "ha ha it looks like a truck" ah, memories

🥺 that's so cute

#leemursays #mine #ask #math #dragon curve

[exnihilo-comic]

no comic friday: in 2018, i noticed that stickers in the printer at work had perforations for tearing, and that you could make hills and valleys pretty easily. so here's a level 6 dragon curve.

#math #dragon curve #paperfolding #origami

[puppetmaster13u]

Prompt 274

You know what is fun? Baby Ghost Jason. You know what could be even more fun? Ghosts are Dragons. 

Jason? Aware of none of this. 

He was on comms, y’know listening and rolling his eyes at Dickwing, who used his real name, really Dick, he mocks. It’s just a stakeout, nothing new there, honestly boring when he could be blowing something up instead. It should have just been a stakeout. 

Yet there’s something suddenly there, something behind him. Something that causes his hair to stand on end and his comms to spark into static like some sort of horror movie. Something, something with clawed hands with corpse-pale skin tipped in black, stained or dead or something else, tilting his head up and up and up as he’s frozen. 

“A child, out here? Alone?” a voice crackles, hisses, hums, and purrs, somehow all at once, unnatural in its tone. He can’t move, he needs to move, he has to move, but it’s like the space around him has gone cold and dead, like he’s stuck in the Pits once more as claws hold his head and his vision blurs. “Sleep, child. Rest- we’ll be home soon.” 

#DCxDP #DPxDC #Prompts #Ghosts are Dragons #Halfa Jason #Not Ghost King Danny #Ancient of Space Danny #Jason: If I just got kidnapped by fae because Dick said my name I’m going to riot #Halfas have human-ish forms #Danny has four arms like Pandora & floating horns like Frostbite & same scale patterns as Clockwork #He’s cooing over the little Star Core Jason #Jordan & Ellie: Oh a new sibling? You give us sibling to tease? Yessss gooood #Pariah looking down at this scrap of a teen now forced into dragon form for his health: Ah yes another grandson #Jason has no clue what’s going on he’s very overwhelmed right now #Danny was not the one to nab Jason but it’s his child now look how cute #sun core dan #moon core ellie #space core danny #star core jason #a lil celestial body flock of dragons <3 #Jason is like a chonky amphiptere-esque dragon #long serpentine with feathered wings but also has legs #six chubby catterpillar-esque ones and long curved talons

[knifeforsale]

WICKED DRAGON DAGGER | LISTING

#knife #straight #dragon #texture #wicked #gold #silver #creature #curved #daggar #wings #novelty

[lucydoodlessometimes]

hello genshin impact fandom. i would like you to please engage with the fic in question. also non genshin fandom tbh this is brain chemistry changing. doodle page of freminet to justify my posting

#lucy doodles #my art #fanart #genshin impact fanart #genshin impact #genshin freminet #genshin fanart #freminet #genshin #pers #toastedfishdish #deep-sea encore #freminet was such a learning curve to draw? #but sooooo worth it #and his colors are so nice #doodle page coloring how you elude me #hydro dragon freminet's design is from their twt #which is the same as their ao3 handle #i forgot his locket. damn it #oh well

[movement-picture-mouth-prevent]

#curve model #narumitsu #degrassi #rusty quill gaming #how to train your dragon #gay furry #batb #bakugou smut #aika sawaguchi #stop asian violence #diary #brand new #the virgin suicides #fate stay night #we heart it

[lesbianslovebts]

I was able to convert a dragon curve into a beading project idea using the square stitch. Basically, if 4 lines of one color enclose a square, then the square will be shaded that same color. Each shaded square represents a bead of that color. If a square is not bound on all 4 sides by one color, then it is the background color. Lastly, any leftover line segments that do not make up a square will be stitched with thread of the appropriate color between the beads. I made up the rough sketch tonight, and tomorrow, I'll post a final drawing of the project plan.

#math #mathematics #fractal #fractals #dragon curve #beading #llbtspost

[blake447]

Getting my arch install looking nice and pretty. Background is a quaternion julia set, and down below we have my dragon curve code that I've been working on. Finally got polybar installed and working, and customized it lightly. Next I'm thinking a compositor so i can have transparent terminals and stuff if I want

#arch linux #linux #unixporn #c programming #c #dragon curve #julia set #fractal #rice

[technician-the]

animation of my dragon curve fractal. this is fractals numbered 780 through 785.

it starts at iteration 3 (the first that was interesting to look at), and goes to iteration 9 (the last that fully fit in the frame).

#fractal #fractal geometry #animated gif #dragon curve

[single-among-away-drive]

#gabbie carter #asexual #akira kurusu #curve model #degrassi #how to train your dragon #batb #bakugou smut #stop asian violence #brand new #fate stay night #the outsiders #jennie kim #evan peters