Draw the intersection of the Attracting Torus Attractor with coordinate plains. More...

Detailed Description

Draw the intersection of the Attracting Torus Attractor with coordinate plains.

Author: Mitch Richling https://www.mitchr.me

Standards: C++20

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Details

I first came across this strange attractor in Sprott's book "Elegant Automation" where it is the topic of chapter 43 starting on page 311. The system is given by the following system of equations:

\[\begin{align*} \frac{dx}{dt} & = a_1 y \\ \frac{dy}{dt} & = -a_2 x - a_3 y z \\ \frac{dz}{dt} & = a_4 y^2 - a_5 + a_6 z \end{align*}\]

Typical values for the constants are \( a_1=a_2=a_3=a_4=1 \), \( a_5=4 \), and \( a_6=\frac{1}{10} \).

On page 315 of Sprott's book is an image of the intersection of the attractor with the \( z=0 \) plane. This program reproduces that image along with the intersections of the \( x=0 \) & \( y=0 \) plane. As a bonus we produce projections of the curve as well.

Reference: Sprott, Julien C. Elegant Automation: Robotic Analysis of Chaotic Systems. New Jersey: World Scientific, 2023.

Definition in file attracting_torus_shadow.cpp.