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

See also: attracting_torus_shadow.cpp

Copyright

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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. In that chapter, on page 315, he has an image of the intersection of the attractor with the z=0 plain. This program reproduces that image along with the intersections of the x=0 & y=0 plain. 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.

Create a gif like this: time convert -delay 1 -loop 0 -dispose previous attracting_torus_shadowM_???.tiff attracting_torus_shadowM.gif time convert attracting_torus_shadowM.gif -resize 50% attracting_torus_shadowM_50.gif time convert attracting_torus_shadowM_50.gif -resize 50% attracting_torus_shadowM_25.gif

Convert color images to BW: magick attracting_torus_shadowZ0.tiff -alpha off -auto-threshold otsu attracting_torus_shadowZ0_BW.tiff magick attracting_torus_shadowY0.tiff -alpha off -auto-threshold otsu attracting_torus_shadowY0_BW.tiff magick attracting_torus_shadowX0.tiff -alpha off -auto-threshold otsu attracting_torus_shadowX0_BW.tiff

Build and load images in eshell on Windows: rm -f attracting_torus_shadow*.tiff; make attracting_torus_shadowM && { ./attracting_torus_shadow.exe ; for f in attracting_torus_shadow*.tiff { start $f } }

Definition in file attracting_torus_shadowM.cpp.