>"When computers revealed all those smaller copies of the Mandelbrot set within itself, Douady and Hubbard wanted to explain their presence. They ended up turni

>"When computers revealed all those smaller copies of the Mandelbrot set within itself, Douady and Hubbard wanted to explain their presence. They ended up turning to what’s known as renormalization theory, a technique that physicists use to tame infinities in the study of quantum field theories, and to connect different scales in the study of phase transitions." https://en.wikipedia.org/wiki/Renormalization https://en.wikipedia.org/wiki/Renormalization Rampant conjecture/speculation: In the future, perhaps some Mathematician might discover a link between Renormalization Theory -- and the Digits Of Pi... since they seem related... More specifically, between Renormalization Theory -- and algorithms for the Digits of Pi. Of which, one notable one is The Chudnovsky algorithm: https://en.wikipedia.org/wiki/Chudnovsky_algorithm https://en.wikipedia.org/wiki/Chudnovsky_algorithm Which leads to Binary Splitting: https://en.wikipedia.org/wiki/Binary_splitting https://en.wikipedia.org/wiki/Binary_splitting Which leads to Hypergeometric Series: https://en.wikipedia.org/wiki/Hypergeometric_function#The_hypergeometric_series https://en.wikipedia.org/wiki/Hypergeometric_function#The_hy... Which leads to Gauss' continued fraction: https://wikimedia.org/api/rest_v1/media/math/render/svg/4d54114465d858bd4de8e8bb87818d19d9e2da38 https://wikimedia.org/api/rest_v1/media/math/render/svg/4d54... https://en.wikipedia.org/wiki/Hypergeometric_function#:~:text=Gauss%27%20continued%20fraction https://en.wikipedia.org/wiki/Hypergeometric_function#:~:tex... https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction https://en.wikipedia.org/wiki/Gauss%27s_continued_fraction Which leads to Analytic continuation of 3F2, 4F3 and higher functions: https://fredrikj.net/blog/2009/12/analytic-continuation-of-3f2-4f3-and-higher-functions/ https://fredrikj.net/blog/2009/12/analytic-continuation-of-3... Which leads to my brain hurting ("Put down that Math book and step away from the Math!" <g>) -- because I can't handle all of this Math for now! :-) <g> :-) But there is this very cool picture there: https://3.bp.blogspot.com/_rh0QblLk0C0/SzEG9q5FxaI/AAAAAAAAAL0/hfg6OZ2QHJA/s400/hcplot.png https://3.bp.blogspot.com/_rh0QblLk0C0/SzEG9q5FxaI/AAAAAAAAA...