#dragon fractal

[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. :]

[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

[publicopinionrp]

Went back to my node setup, got the dragon curve working.

[belghast]

Failing Can Be Fun - Another round of Fractals with Friends, and Commanding a completely doomed Dragon's End map in Guild Wars 2.

[anarkhebringer]

Man I don't even talk about my Astral Ward Trahearne enough to be itching to rant about the whole-ass dynamic he has with a Canach fractal that's out to kill him and has a sort of possessive urge to control him

[skadream]

heres a bunch o drawings of space filling curves over the years

heres a selfie from like 2015 w some dragon curves in the bg. i can probably find more in my box of old sketchbooks n shit

[codedrawn]

Dragon Curve Again!

Ok, so I know that I've been repeating things a lot, but I really wanted to kill a few hours so I used that as an opportunity to practice C and since I've been doing image stuff lately that was a obvious choice. I didn't make a drawing library for this one, I just set each endpoint to black and set the number of iterations up high enough for that to fill everything in.

I ran into an issue due to running the line splitting recursively over a linked list of points and after running the line splitting like 17 times there was so many lines I filled the stack, so I switch to doing it iteratively and all was well. More specifically, this version ran the line splitting 18 times, the minimum for it to actually fill in, and it has 262145 points so that's how many recursive function calls were attempted.

The reason I wanted to do a linked list for the points is because I need to insert points between other points constantly and when doing it in rust vector I constantly had to copy values from one vector to another and this solution avoids it. I'm not actually sure if that is enough to actually make linked lists the more performant solution but, between needing to insert values in the middle of the list thousands of times and always needing to iterate through the list instead of indexing, I doubt the stars will align better than this.

Aside from those caveats, the algorithm is the same, but I've decided to include a small snipped under the cut since its taking me so long to actually host my code.

This image (made with carbon.now.sh) shows the line splitting part of the algorithm. In short, take the angle between the two points, rotate by 45 degrees with it being clockwise or counter-clockwise alternating, then find the distance the new length should be, which is equal to the length of the first line times the sine of 45 degrees, aka one over the square root of two, which is absorbed into the other square root for reasons that I can't remember because I found it using another method that I also can't remember and had written on a whiteboard that my boyfriend has drawn an among us/gravity falls comic on, but it's provably correct so I don't really care.

The rest of the code is just initializing everything, storing the results of this, then writing the pixels. I could optimize it more but its pretty fast as is so that isn't a priority.

[alumbradoss]

Phoster Fragments - Fractal Memories

The memories hit me like a wave. It wasn’t sudden, but more like a distant song growing louder, a melody I hadn’t heard in eons. I wasn’t on Earth anymore—not really. My body was still there, sitting in the stillness, but my mind was elsewhere, traveling across time, drifting into forgotten realms. The air around me seemed to shimmer as the veil thinned, and I found myself standing on the edge…

[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.

[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

[argonianfeather]

think it's funny that i made Moonlight my most "straight-edge" character, considering she's the "I have been practicing necromancy since I was 6 and suck peoples dry of blood. regularly." protagonist of the bunch

[a-shade-of-blue]

Can you donate the price of a coffee so that 10 children (and a 2-year-old baby) can have food to eat? (and at the same time get the chance to win a handmade phone charm made with freshwater pearls?)

I have been talking with Mahmoud (@mahmoudfamily1) and he is really worried about his family. There has been continuous attacks on Nuseirat, where his 17 family members (including 10 children and a 2-year-old baby!) are staying. Just a few hours ago, an air strike in Nuseirat has killed 6 children and their parents! A lot of the casualties coming out of Gaza are children, and I'm really worried about these 10 little children at Nuseirat.

Moreover, their tent has just been bombed, destroying everything they have and leaving these 17 people with nowhere to sleep. Basic necessities are 300% more expensive than usual. With such astronomical price and little funds, they do not have most daily necessities. How are they going to cope with the coming winter? With no shelter to shield them from the rapidly dropping temperature and the heavy rain, with no clothes to keep them warm, and with little food and clean water too!

Low Funds! Only $1,627 CAD raised of $80,000 goal! Last donation was 14 hours ago!

This campaign is #117 on @/gazavetters vetted list. Also vetted by association!

I'm also hosting a freshwater pearl phone strap raffle to raise funds for this campaign (UK only)! Click here to enter after you donated!

Tagging for reach. Please message me if you want off the mailing list. We thank you in advance.

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[quintiliusheartripper]

Im excited too because while there may be some rushed or flat story beats for a variety of reasons I love the world setting of tyria. I love seeing what unfolds and how it affects my characters since I dont have a commander oc (not entirely atleast). Characters who are affected by the events in ways that can be really explored.

not to be an enjoyer of guild wars 2, a positive thinker, a game liker, but i AM excited for expac5. i like that teaser image a lot. i like just the thought that we will get new areas and new threats. i will also be believing that anet learned from palyer feedback for soto and will improve. not to be a positive pnancy but i think i will be enjoying that

[gyroncraft]

Minecraft Fractal Experiments p1

featuring dragon curves, sierpinski triangle, and menger sponges!

[gone-fish-mode]

hello beasties! apologies for the mass tag- but I thought it would be the best way to get the attention of everyone who showed interest in a nonhuman news letter!

Currently, I am opening up applications to help me out with the newsletter and email updates + subscriptions! You can do both, you can only do one, it doesn't matter.

The newsletter is not ready to open submissions and the website isn't done yet, but the ball is approaching the edge of the hill and, god willing, is about to start rolling.

there are no real requirements to be apart of the staff, I just ask that you are a) nonhuman, b) 16 or older, and c) able to use discord.

If you really wanna help, but don't want to use discord, just send me a dm or comment and we can find a way for you to be apart of this without the discord.

All the information you need should be in the google forms. I'll go in tonight and start adding folks to everything.

If you have questions, comment!!! dm me!! I know the forms say email, but honestly we're not to the point where email is preferable.

There is no age restriction on the updates or subscription list!

updates + subscription

@thatonefurryartist

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@that-dreaming-dragon

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[luli-lads]

~ Masterlist ~

Predictions before he was released

Drabble before he was released

Unnamed smut - Before we knew what his Evol was

Period sex (smut) - Before we knew what his Evol was

Dragon!Sylus + Part 2 (fluff/smut)

Predictions before he came back from the explosion

He comforts you during a thunderstorm (fluff)

He catches you reading fanfics (smut/funny)

Know Your Place (smut)

"The Snow King" retelling (angst)

When he's drunk (fluff) - Written before we got Absolute Zeal

Kissing him (fluff/comfort)

Fem!Dawnbreaker (smut)

What is this Feeling? (Zayne x Carter smut)

Fractal Library Q&A Theories - Written before Death and Rebirth was released

A typical night in his life (smut)

Sneaky Evol use (suggestive)

Jumpscaring him (funny/cute)

"The Little Mermaid" retelling (angst)

A Sea God's Wrath (angst)

Drawing with him (fluff)

Look, no hands (smut)

You married someone else (angst)

You died (angst)

You died again!? (crack)

My grandma sold me to Love and Deepspace!? (crack)

If they all met each other (crack)

You turned tiny + Sylus' + Caleb's (fluff)

They turned tiny (fluff)

They turned into animals (fluff)

Kissing them all over their face (fluff)

Zayne and Sylus as your classmates (funny)

Starapplemc headcanons (bit of everything)

Daily shorts

SMAU Masterlist

Playing with Mephisto + Part 2 (fluff/crack)

Playing the claw machine with Luke and Kieran (fluff)

Playing Kitty Cards with Viper (fluff/funny)

Royalty!reader x gardener!Jeremiah (fluff)

Nero unfinished drabble (smut)

A Weekend with Nero (pwp - porn with plot)

My pen drawing of Mephisto