Скачать или смотреть Deeper fractal zoom from the highest infinite

In this visualization, we zoom into a fractal arising from the highest infinite.

The underlying algebraic structure is known as a Laver table. The n-th Laver table is the unique algebraic structure with underlying set {1,...,2^n} and fundamental operation * where x*(y*z)=(x*y)*(x*z),x*1=x+1 mod 2^n for all x,y,z in {1,...,2^n}. The elements in the Laver table can be partially ordered by the inclusion relation on the subalgebras that they generate.

We reorder the elements in the Laver table so that x precedes y if there is some m with x=y mod 2^m but where x is in {1,...,2^m} mod 2^(m+1) and y=x+2^m mod 2^(m+1). With this reordering of elements, the Laver table partial ordering forms an image. Since we have an image for the n-th Laver table and since these images cohere, they form a zoomable fractal, and we zoom into this fractal.

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