Just Discovered The Site “underground Mathematics”, And Only Now I Feel Like Ive Entered The Dark

this. this is me. every single morning.

🍂*wakes up and stretches realizing my new form*🍂

Mathematics people interested in either learning about the Peano axioms of natural numbers (how do you prove a+b = b+a) or interested in learning a proving assistant (Lean) should DEFINITELY check out the natural number game. This is a game which teaches you both of these things step by step, and has you construct the natural numbers and their most important properties from the very basic axioms. Even if you just like logical puzzles and are interested in a bit of mathematics you should check it out!

this deserves to be its own post. like yes. totally endorsed.

touching grass is not enough sometimes. sometimes what you actually need to touch is a math textbook

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I realized I hadn't shared this here yet! Here's my 3D printed Quaternion Julia Set! See I first learned of these things reading about it from a pretty well known graphics programmer Inigo Quilez. Theirs are a lot prettier! But yeah, if you're familiar with Julia Sets and the Mandelbrot set already, this is basically that but we use 4D complex numbers called quaternions instead of the regular old complex numbers.

The original shaders I used to render them were unity CG/HLSL implementations, but this particular one is from a GLSL implementation over on my shadertoy you can find here: https://www.shadertoy.com/view/tdt3W8 It isn't exactly the same one that I've printed here (I've long lost the exact seed) but it is reasonably close. The way I printed it was I stole some marching cube code for blender and just plugged in the SDF function derived by Inigo Quilez, tweaked the values and eventually got a mesh I can print!

This uh, isn't the one I used lol. It did take a few tries to get one that was both visually interesting and also printable. In fact i wasn't even using the marching cube algorithm at first. I was using Poisson Surface Reconstruction with a python script that casted points to form a point cloud. Basically I was attempting to create a mesh like you would with photogrammetry, just with an abstract object rather than an actual thing or place.

The results were, well not good lol.

*Continues digging through box* I know its around here some where, I should have the one that works. Okay this still isnt it but this one is using the same method, I just wanted to use this for a vrchat world instead of using it for 3D printing. It gets the point across lol

But yeah. 3D printing is really cool if you're into a bit of math

Any point on torus lies on four circles on torus.

A/C unit failed. Repair scheduled for Tuesday.

I want to buy 10kg of dry ice and put it in my house.

Questions:

Will it have an appreciable effect?

Will my cat die?

Jim Holland Green Room.1955