This chart shows the logarithmic growth of maximum possible entropy ($H_{max} = \log_2(N)$) as the number of states (N) increases. The red dot indicates the maximum entropy for the current number of states in the simulation.
This graph shows the entropy of a single coin flip. Entropy is lowest (0) when the outcome is certain (an unfair coin that always lands on heads or tails). It reaches its maximum (1 bit) when the coin is fair (p=0.5), representing the highest uncertainty.
The vector field represents the curvature of spacetime as dictated by Einstein's Field Equations. Each arrow shows the direction of the "geodesic," the straightest possible path an object can take through this curved space. The flowing particles represent matter ($T_{\mu\nu}$) following these paths.
Light rays are also bent by gravity. They appear blue (blueshifted) when falling towards the gravity well and lose energy, becoming red (redshifted) as they escape.
If you find the content on this website useful for your research or work, please consider citing it. You can use the following BibTeX entry:
@misc{TaalPages2025,
author = {Taal, Jasper},
title = {Math, Statistics and Machine Learning Visualizations & Projects},
year = {2025},
url = {https://jtaal.github.io/}
}