Creating interesting images by connecting the partial sums of a series involving the exponential of complex numbers.

When does log x equal x with the decimal place moved? First we look at the problem for base 10, then for more general bases.

A general recipe for creating randomly-generated fractals that tile the plane.

Learn why autoregressive flows are the superior density estimation tool for high-dimensional data The post Cracking the Density Code: Why MAF Flows Where KDE Stalls appeared first on Towards Data Science. Generated by RSStT. The copyright belongs to the original…

Knuth defines the twindragon fractal to be the set of complex numbers that are "fractions" in base 1-i. Implemented in Python code.

Pick's theorem computes the area of a figure drawn on a grid by counting the number of grid points inside and on the perimeter, but the formula isn't obvious.

Variations on Knuth's twindragon fractal by rotating the base.

Learn APE, RoPE, and ALiBi positional embeddings for GPT — intuitions, math, PyTorch code, and experiments on TinyStories The post Positional Embeddings in Transformers: A Math Guide to RoPE & ALiBi appeared first on Towards Data Science. Generated by RSStT.…

Panning a spherical image is just a horizontal roll, but tilting it vertically is much trickier. Let's see the math! The post The Math You Need to Pan and Tilt 360° Images appeared first on Towards Data Science. Generated by RSStT. The copyright belongs to…

Riemann's P-symbol is an intriguing/intimidating piece of notation. It denotes a solution to a very important class of differential equations.