a simple way to fingerprint a language-

take a bunch of text in the language, and every time one character occurs after another, connect them with a line from the left side to the right side

here is English after 70 million characters some more languages

an app where kids can view their lego models as if they were real and full scale

I made these with Stable Diffusion - pushing the photo away from 'lego' and towards 'photograph'

we can now create infinite zooming fractals using Stable Diffusion's machine learning models

for this one I entered "scottish coastline satellite image" for this one I put "path going into forest"

give each pixel a random Pokemon type, and then battle pixels against their neighbors, updating each pixel with the winning type (using the Pokemon type chart)

we quickly see areas of fire > water > grass > fire, electric sweeping over, ground frontiers taking over etc etc this is a cellular automaton, inspired by the rock-paper-scissors automaton-

https://twitter.com/AndrewM_Webb/status/1236274167437197320

no matter how chaotic and unstable the orbits of these three gravitational bodies are, their centre of gravity (centroid of the triangle) always remains stationary and fixed in space in general the centre of gravity moves at a constant velocity, but I ensured this velocity was zero for these simulations

did you guess what shape is hidden in the circumference of this wire? equation of the wire

visualizing prime factors more numbers

WaveGrad by @cnxhk et al is a clever new neural net for generating speech. It starts with random noise, and iteratively denoises, essentially hallucinating a voice in the noise. Listen to the voice emerge, as the number of iterations increases with time 🔉 The WaveGrad paper: arxiv.org/abs/2009.00713

creating an infinite spiral zoom using complex analysis. The map z -> z^(x + i y) warps the image so that it can be infinitely repeated inside itself we can get different spirals by changing the complex exponent. Here's a double spiral

I managed to make a pretty good 3d model of the Julia set ring. Is anyone interested in helping me 3d print it? I first created code to generate the perimeter of a Julia set in mathematica, by repeatedly applying the inverse map to (1, -1, i, -i). Then I wrote some python code to generate a .obj 3d model, and rendered in blender

images as bar charts of red, green, and blue @standupmaths covered this really well

if a black hole passed in front of a mirror, what would its reflection look like? these could be considered its reflections

a ring built from the Julia sets that lie along the main cardioid of the Mandelbrot set - version 2 @Shadertoy source shadertoy.com/view/wd2BDR

a ring built from the Julia sets that lie along the main cardioid of the Mandelbrot set the Julia sets along the main cardioid of the Mandelbrot set, from which this ring is built

surprising patterns from slicing the Menger sponge fractal @Shadertoy source code shadertoy.com/view/3sBBzm

find the centroid of a triangle, by connecting the corners to the midpoints. this construction creates 6 new triangles. repeat this process eventually creates triangles of every possible shape

ams.org/publicoutreach…

a cardioid is formed by light rays radiating from a point on a circle- the same shape obtained from rolling a circle around another. Here is a visual proof for why

a hexagonal tile turns blue at each step if it has exactly one blue neighbour @Shadertoy source code shadertoy.com/view/3dffzl

spherical circles cast circular shadows when a light is held at its north pole source code on @Shadertoy shadertoy.com/view/tdlBRj

a method of drawing infinitely many touching circles the construction with the rectangle of constant area is circle inversion in disguise

composing two Julia sets. Top left is the Julia set for f(z) = z² + c, with varying c. Top right is the set for g(z) = z² + c, for a fixed c. The bottom is the set for f(g(z)) a higher resolution frame