Lenia – Mathematical Life Forms

Lenia (from Latin lenis, “smooth”) is a cellular automaton, like Conway’s Game of Life, but with continuous states and continuous space-time. It supports a great diversity of complex autonomous patterns or “lifeforms” bearing resemblance to real-world microscopic organisms. More than 400 species in 18 families have been identified, many discovered via interactive evolutionary computation.

Paper: arxiv.org/abs/1812.05433

Code: github.com/Chakazul/Lenia


Making a Heart with Maths

Inigo Quilez (iq) explains how to model a simple heart with mathematics. Shadertoy code and real-time version can be found here. I love how he embedded the model into the video. Need to explore how to develop plugins for AfterEffects. Jim Fowler, Professor at Ohio State University applied a similar technique in his Calculus course on Coursera. He used the old ray tracing tool POV-Ray with ArUco, a library for augmented reality applications.

KaTeX, Khan Academy's Math Typesetting Library

Khan Academy has published the fastest typesetting library for the web. IntMath’s KaTeX and MathJax comparison demo shows some impressive performance improvements. The demo page took 177 ms to process on my laptop. The MathJax version on the other hand took 4777 ms. The performance comes at a price that not everything is supported in KaTeX (yet). I wish aligned equations were supported, but I can live with it. Until I run across more serious problems I’ll happily use KaTeX instead of MathJax.

Zequals and the Art of Estimation

In this Numberphile video Rob Eastaway presents Zequals which can be useful if you need to compute a quick estimate, for example to find out if your calculation is on the right track. The idea is to ruthlessly round every number to just one significant digit. For example: 3 * 7 = 21 zz 20 7 * 8 = 56 zz 60 436 * 68 zz 400 * 70 = 28000 zz 30000 The actual answer is 29648 and surprisingly close to the zequal result of 30000.