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Matt Henderson Profile picture
@matthen2
Apr 12, 2020 • 4 tweets • 1 min read • Read on X
the centre of a logarithmic spiral traces a straight line as it is rolled. this means a pair can be used as unconventional gears
There is no slipping between the two gears, and the point of contact moves at a constant speed from the centre of one gear to the other (with a discontinuity at each turn).
The slope of the straight line traced by the centre is called the spiral's pitch. A golden spiral is a logarithmic spiral with pitch 17.032°
#mathematica code for this animation: pastebin.com/F2SPAWJa

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More from @matthen2

Matt Henderson Profile picture
Apr 3
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 Image
some more languages Image
notice that similar languages look similar Image
Read 8 tweets
Matt Henderson Profile picture
Sep 3, 2022
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'
Read 6 tweets
Matt Henderson Profile picture
Aug 30, 2022
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"
"new york city buildings looking down from a distance"
Read 8 tweets
Matt Henderson Profile picture
Jul 2, 2022
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-
in this version, pixels only battle against the four neighbors to the north, south, east, and west (and not in the four corners)
Read 6 tweets
Matt Henderson Profile picture
Oct 30, 2021
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
for more 3-body animations- check out @ThreeBodyBot
Read 4 tweets
Matt Henderson Profile picture
Aug 6, 2021
did you guess what shape is hidden in the circumference of this wire?
equation of the wire Image
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

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