#pretty fractals

[violetfractal]

You can generate Sierpiński carpet (the 2D analog of Menger sponge) at home! I started with addition modulo 3 and some conditional formatting in Excel.

I left the modulus configurable. Powers of 2 produce simple tessellations instead of fractals, so the first viable fractal is A1=3. Here’s the modulus 3 image at 729x729 resolution:

This is the standard sierpinski carpet. But starting with modulus 5, higher primes are going to give us some trippy Menger-analogs with intricate self-similar geometry. Let’s dive in:

Modulus 5

Modulus 7

Not all composite numbers are duds! Mod 9 is beautiful with its single order 3 subgroup.

But Mod 15 is not so much a fractal as a self-similar glitch. The subgroups of order 3 and 5 are all jumbled together!

Modulus 17

Modulus 19

Modulus 23

Modulus 29 with 707281 cells. (That’s 29 to the fourth power!) And that’s the limit, because Excel is running garbage collection nonstop trying to compute any more of the image. Excel 2010 was limited to 2GB of ram and we are out. I call this collection of renders “seafloor”.

Original Date May 7th, 2023 11:16pm

[decamarks]

Man what the fuck is going on in Snowpoint City

[euphorictruths]

Crystal Plant- Eric Ton

[one-hit-boy-wonder]

Dick had the hardest time adjusting to Hudson U because he kept thinking all his eccentric professors were up-in-coming supervillains when in fact they were just normal guys who wanted to infodump about fractals

[gnatlistens]

heard SOPHIE's love me off earth at evita manji's dj set recently,... i'm still feeling so emotional haha. LOUD! MUSIC! blasting through my veins, the PEOPLE and that sense of community, exploring more of myself,

[jfishburnartworks]

"Time flies"

[eyes-that-decieve]

Tal and Dreaming, one of the guys who was in the corridors with you came in for a statement. Just thought I'd let you know.

Recorded it, I got permission to send the transcript (the actual file corrupted and broke after playing it back once, I didn't mean to record it on my phone), so if anyone wants to read it!

[Recording begins. The device seems to be in a pocket, the view is tilted and obstructed about halfway down by a table. A visibly shaken boy, maybe 17, sits on the other side of the table. His skin is pale and has an almost gray look, possibly the lighting. His brown eyes dart around nervously as he fidgets, occasionally using one hand to fix short black hair, three pronounced white streaks near his temple that appear to be natural.]

Styx: Why here, and not the institute?

Penn: I got pulled in through a door over there, you have to know if that happens in your place, right?

Styx: Right. Want to tell me about it?¿

Penn: Yea- Yes.

[Sound of a quiet breath, a few muttered words from Styx]

Penn: I was in here for a coffee before catching the bus home- [Speaking very quickly, cutting himself off before speaking much more normally.] Long day and all. There was a really brightly painted door over there. Black background, neon I believe?

[Penn gestures to one wall, his hand going out of frame]

Penn: I hadn't been in here before, so I didn't think it was out of place. It just felt a little off. It opened from the other side, someone beckoning me, claiming something about free food. When I come to think of it, I can't remember what they looked like. The second I stepped over the threshold, the door snapped shut and was gone.

The person who led me in was gone too. I turned around again and a flippin' dragon was right in front of me! Thought it was kinda cool for a second, all shiny black scales and purple and yellow eyes. It laughed for a second, in two different voices? This sounds ridiculous.

[Penn pinches the bridge of his nose with two fingers, but keeps talking.]

Penn: They jumped at me and I started running. They didn't chase me. The whole place must have been too confusing, even for a dragon. It was like the door, everything was dark and neon at the same time, edged in bright colors. It all hurt my eyes, I ran straight into a lamppost right in the middle of the path after a few minutes. I kept walking, but my head still hurts from it. That must have messed up my eyes worse, because everything got more confusing. Branching paths, curving back on each other. I swear I ran into that same lamppost three times. I was going in circles.

At some point it hit me. And by 'it' I mean a person. The whole place had been shaking for a few minutes, then someone comes hurtling down from the ceiling and knocks me to the ground. They had. . . Wings? Feathered ones, I remember the sound. Other than that, I don't remember what they looked like. 'If nothing was a person' comes to mind, but I don't remember why. They immediately ran over to a tree while I was still reeling, and straight up punched the thing. The whole place shifted, from dark and neon to colorless. The floor was gone, the trees were gone, the little buildings were gone.

I don't know how long I wandered that emptiness. I thought I was going to die there. Or at least almost die, again. At some point I saw a door open in the distance, and the same dragon walk in. It was talking to someone else, still outside the door. It started painting on the void with its tail. I headed over there, because of course, it's something different from the void I'm stuck in.

Another creature came through the door. It looked kinda like a little kid? Green dress, big smile, curly red hair. It was talking with the dragon, then seemed to notice me.

Asked if I knew who it they were, and where I was. It shoved me back towards the dragon. I looked up at it, and it had too many teeth. Far too many. The dragon pushed me back towards the kid, and I ran. I heard the child say something about no way out and no one coming for me. The dragon followed after that, though I could just see its eyes, two one one side, purple and yellow, and blue on the other. Those and it's smile. Like a Cheshire cat? I turned a different way from it, I thought it was going to bite me.

The child cornered me. It said I wasn't myself, I was gone. It shoved me towards the dragon, who I didn't even realize was behind me. It's wings closed around me. No way out. No escape. I thought it was going to kill me.

[Penn laughs quietly, almost hysterically]

Penn: Next thing I know, I'm waking up on the sidewalk.

[Pause]

Styx: That it-? [Penn cuts them off]

Penn: That makes three, you know.

[Slight fabric sounds, camera is shifted slightly as if Styx is leaning forward a little.]

Penn: Three times I've nearly died in the past week. Almost hit by a car, almost fell off a balcony, ALMOST got killed by a dragon. Each time, all that's running through my head is 'is this when my luck is going to run out?' I'm not a cat, I don't have nine lives!

[Styx makes a quiet 'hm' noise.]

Penn: I don't.

[Long pause]

Styx: Statement ends.

[They clap their hands, standing up. Camera view is shifted up, no longer obscured by the table.]

Styx: Alright, thank you! [Sarcastic] I will keep dragons out of my cafe in the future.

Penn: That's it? That's all you're going to say?

Styx: Yeah, that's about it. If you have any more near death experiences like that, feel free to let me know!

Penn: Oh. Okay.

[Penn stands up, video cuts]

[sihdiel]

one of the last of 2023. i like the sketch but i dont know if i will ever go back to finish it

[violetfractal]

"moth feathers"

May 4th, 2023 6:03pm

[euphorictruths]

One Drop- Blake Foster; 2022

[jfishburnartworks]

"Walking home from school"

[murderthegods]

I hate waking up early not only do I have to set alarms and wake up fifteen times before the thing I have to be up for I have to sleep terribly and dream repeatedly about being late for the thing I'm supposed to wake up for

[puppetboysx3]

don't understand how fractals work, but they are genuinely so cool

[13thpythagoras]

I can add some nuance here as we've learned more

Our galaxy is being pulled toward something called "The Great Attractor" which is the gravitational focal point of our neighborhood of the universe, called the Laniakea Supercluster. Why is the great attractor pulling everything toward it? Maybe someone charismatic lives there I dunno

Additionally, evidence is coming out that conclusions about a collision course trajectory between Andromeda and the Milky Way were overblown, it was originally just a blueshift that we "blew" out of proportion (heheh) but it's actually unlikely that our galaxies will merge though we're talking about what will happen in over 10 billion years at this point

Our solar system moving through space..

[proximacentaurib]

There comes a point in the study of everything where you realize that you're in too deep, too far gone to see anything that can be meaningfully discerned from anything else. So, too, have I analyzed myself to the point of abstracting away any and all details of my person, to that point of turning my eye inwards and seeing only myself sitting back at the start with the single unanswerable question of "Who am I?"

[violetfractal]

“Thessal”

C3=MOD(C1+C2+B2+B3+A3,3). The triangles along the main diagonal have side lengths (in cells) of 1, 4, 13, 40, 121, 364 and so on. In base 3 those numbers are 1, 11, 111, 1111, 11111, 111111 and so on! The other triangles may have powers of 3 as their side lengths.

original date May 22nd, 2023 6:03pm