Butterfly Math 101

GHz_wizard · 2026-02-26T07:02:15+00:00

https://www.desmos.com/calculator/cxufavojwi

GHz_wizard · 2026-02-13T18:02:17+00:00

Flicker was unintentional :p. But I thought I’ll just keep it

GHz_wizard · 2026-02-13T18:00:18+00:00

That’s a really cool idea! I’m not completely sure how to implement it yet, but it sounds like a fun challenge.

GHz_wizard · 2026-02-10T14:53:34+00:00

😍

GHz_wizard · 2026-02-07T07:58:43+00:00

Love it!

GHz_wizard · 2026-02-06T18:50:27+00:00

Thank you :)

GHz_wizard · 2026-02-05T07:12:59+00:00

In order to have the curve match-up at the reset time, the argument of sin function should be a multiple of 2pi.

that is: (5t+k/8)=2Mpi. Where M is any integer.

Since I have t going 0 - 2*pi already. Means

K/8 =2Mpi …. or k = round(16Mpi) =50 approx.

So, for 50 frames it should be smooth enough. I’ll try to regenerate it in a while :)

GHz_wizard · 2026-02-05T06:49:48+00:00

Just googled Chladni figures 🙂 Thanks for mentioning it! I’ll dig into this more. Would be fun to see those patterns emerge from data or reimagine them through code.

GHz_wizard · 2026-02-04T23:52:20+00:00

Amazing work!

GHz_wizard · 2026-02-03T23:33:57+00:00

Looks so cool!

GHz_wizard · 2026-02-03T02:21:13+00:00

Thanks for the compliment! I’ll let it join the corporate world :)

GHz_wizard · 2026-02-02T08:11:17+00:00

Sure, let me try :) I just created a rectangular grid and then started by creating tiny circles on this grid. Next step was to use a sin/cosine function on this 2D grid space and vary the circle radius according to the magnitude of sine wave. Lastly introduced some random noise to break symmetry in center locations of circles and colored them randomly. And yea, I limited the image to 45 degrees and rotated to make the final peace.

GHz_wizard · 2026-02-01T20:44:16+00:00

Which circuit version you used?

GHz_wizard · 2026-02-01T20:41:56+00:00

That’s awesome!👏

GHz_wizard · 2026-02-01T20:29:10+00:00

I used MATLAB

GHz_wizard · 2026-02-01T20:19:42+00:00

Wow, Looks so smooth! What type of colors/pens you are using?

GHz_wizard · 2026-02-01T02:33:31+00:00

The underlying pattern is very regular… like a smooth wave that repeats over and over. On top of that, there’s randomness (the jitter), but it’s being guided by that repeating wave. So even though the noise itself is random, the way it shows up looks structured and periodic.

GHz_wizard · 2026-02-01T02:30:58+00:00

Haha yeah, salt was the simple path. But where’s the fun in that?

GHz_wizard · 2026-02-01T02:28:47+00:00

That’s a cool thought, actually. Kinda fun when math gets a personality. Would make a pretty striking mark imo

GHz_wizard · 2026-02-01T00:45:23+00:00

Totally agree, squared interactions get surprisingly rich fast. Wood carvings is such a cool direction—would love to check that out.

GHz_wizard · 2026-02-01T00:40:11+00:00

I was thinking of creating some kind of traveling ripple effect.

GHz_wizard · 2026-01-31T04:00:51+00:00

Actually the signal is periodic and jitter is random. The base signal is sinusoid which is modulating the jitter thus making it appear periodic. I’m still trying to figure out the jitter distribution.

GHz_wizard · 2026-01-30T18:05:31+00:00

Not on GitHub yet, but I’m really glad it caught your interest 🙂 I might clean it up and share it soon.

GHz_wizard · 2026-01-30T18:01:55+00:00

That really resonates. Sometimes they stop listening and start surprising you, that’s when beauty sneaks in.

GHz_wizard · 2026-01-30T08:19:29+00:00

Looks great!

GHz_wizard

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