Take the parity of the indices of the terms of the continued fraction of Liouville's constant that equal 8. For odd turn left, for even turn right.
What do you get?
The Dragon curve appears, again. It's everywhere.
This works with indices of terms equalling 1 too (for 9 you'll have to ignore the first digit)
This entire fractal is fully defined by these two transforms being animated.
https://timhutton.github.io/mobius-transforms/dfs_recipes.html?id=special&ta.x=1.870000&ta.y=0.080000&tb.x=1.870000&tb.y=-0.100000&tab.x=1.790000&tab.y=-1.948000
The swirliness of the transforms themselves (they are 'loxodromic') seem to make the fractal visually appealing. One day I will try using fluid dynamics motions to explore this idea.
The Second Edition of
Make Your Own Mandelbrot
has a new chapter explaining the Distance Estimation Method which overcomes the loss of sub-pixel detail.
Check it out!
https://www.amazon.com/dp/B0CQS8JYJC
all the code is freely available:
https://github.com/makeyourownmandelbrot/Second_Edition
