Show HN: Hopalong Attractor. An old classic with a new perspective in 3D

Pixel-Based Density Approximation: Hopalong Attractor (Python)

Abstract

Historical Context

The Hopalong* attractor, authored by Barry Martin of Aston University in Birmingham, England [2],

was popularized by A.K. Dewdney in the September 1986 issue of Scientific American. In Germany, the Hopalong attractor gained further popularity through an algorithm called HÜPFER in the article Psychotapeten published in Spektrum der Wissenschaft. [3].

*Nicknamed by A.K. Dewdney.

The Hopalong Attractor Functions

The mathematical definition of the Hopalong attractor is given by the following system of recursive functions, defined in [2]:

$$ \large \begin{cases} x_{n+1} = y_n - \text{sgn}(x_n) \sqrt{\lvert b x_n - c \rvert} \\ y_{n+1} = a - x_n \end{cases} \large $$

Where:

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