# Japanese fractals from Hokusai to Shishikura and beyond

The above picture is Katsushika Hokusai (葛飾 北斎) famous painting The Great Wave off Kanagawa

Mitsuhiro Shishikura famously proved that the Hausdorff-Besicovitch dimension of border $\partial M$ of the standard Mandelbrot set of $z\rightarrow z^{2} +c$ is 2. (meaning that it’s the frothiest possible ‘curve’ there can be, basically)

Tomoki Kawahira has done some work on Riemann’s zeta function and Newton’s method.

Shigehiro Ushiki has created some awesome visualizations (movies) of the complex Henon maps

Kentaro Ito has visualized 4-dimensional Kleinian punctured torus groups.

Yoshiaki Araki and Kazushi Ahara have made movies
of 3 dimensional quasifuschian group limit sets.

And there are also the Lakes of Wada

And for a bit of amateur (though far from unbiased) bit of cultural anthropology: I’m not the first to notice this, though we are way behind when it comes to the cultural anthropology of mathematics. It is arguable that this kind of research in Japan has as its parent the Sangaku / temple geometry problem. I am not an art historian or a cultural anthropologist of mathematics, but future mathematical cultural historians may find this: a good jumping off point