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Matt Henderson

30 Oct, 4 tweets, 2 min read

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

@ThreeBodyBot

for more 3-body animations- check out @ThreeBodyBot

https://twitter.com/ThreeBodyBot/status/1453966295817338885

final frame high res

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More from @matthen2

Matt Henderson

@matthen2

6 Aug

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

equation of the wire

@WolframResearch

or, more succinctly in @WolframResearch #Wolfram language:
RotationTransform[ t, {0, 1, 0}][
Join[ Entity["PopularCurve", "PiCurve"]["ParametricEquations"][t] /
500 + {3, 0}, {0}]]

Read 5 tweets

Matt Henderson

@matthen2

31 Jul

visualizing prime factors

more numbers

My old version of this

blog.matthen.com/post/120471240…

Read 4 tweets

Matt Henderson

@matthen2

11 Sep 20

@cnxhk

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

the video shows mel-spectrogram features that are used to guide the denoising and specify the speech to produce. These could be the output of a text-to-speech system

Read 4 tweets

Matt Henderson

@matthen2

15 Jul 20

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

#mathquiz what type of spiral is this?

Read 4 tweets

Matt Henderson

@matthen2

6 Jul 20

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