Conversation

Alright, math thread time, followed by a cry for help

Apr 15, 2020

Starting with a random point, then repeatedly walking halfway to one of three points, plotting where the point lands each time, gives you the sierpinski triangle. It's neat, here's a cool animation for 5 points:

Quote Tweet

David Berardo

@SarlCagan93

Apr 14, 2020

GIF

One my favorite ways to make fractals. The red point moves halfway to one of the corners randomly, and thats it!

Show this thread

Then

asked me: "hey, what if, instead of jumping to a random choice of three points, you jump to a random point on the edge of a circle?" Some context, if you do the above algorithm for 4 points, you just get a sad flat square. I was fully expecting a sad flat disk.

Ashley

@khyperia

Apr 15, 2020

I whipped up my crappy implementation, and this image came out. What the butts?? There's a hole in the middle? ... wait, is there a ring of darkness around the middle there???

Ashley

@khyperia

Apr 15, 2020

This had to be artifacts of my garbage GPU RNG implementation, so I reimplemented it on the CPU, with good RNG, and cranked the samples way up. ... oh. oh dear.

Ashley

@khyperia

Apr 15, 2020

Okay, what if we take a slice of that data? As in, start at the center, draw a line to the right, and plot the value that line goes over. Graph it! ... what???

Ashley

@khyperia

Apr 15, 2020

okay, let's take the derivative of that graph y'know that looks vaguely fractal-like somehow, those humps look recursively similar, aaaAAA, I'm not okay

Ashley

@khyperia

Apr 15, 2020

so uh, does someone know what the heck is going on here? or can someone work out an analytical solution to whatever the *heck* that graph is doing?

Replying to

If I understand correctly, the whole in the middle you can only end up at if you are already at the edge of the circle, and you randomly pick the other edge. The chance of this vanishes.

Replying to

and

That circle is odd though. So I guess the question is: why is it so hard to arrive there?

4:16 PM · Apr 15, 2020Twitter Web App

Replying to

and

I think I know: you can only arrive at the r=1/2 point if you start from the center, and by the previous argument it is hard to get there in the first place. I think this then applies recursively.

Replying to

and

Yeah, to be in the middle, we need to start somewhere near the edge then pick the opposite side. To be near the edge, it would mean we need to keep picking the same point on the edge of the circle or it's neighbors.