一个与其平移有Cantor集交的平面自仿铺砖(英文)

A Planar Self-Affine Tile with Cantor Set Intersections with Its Translates

给出一个平面自仿铺砖,虽然在它生成的自仿铺砖中,它只有边邻居和点邻居,但它仍与自己的某些平移有Cantor集交.这显示Cantor集交在这类分形集合中的普遍性.

We give a planar self-affine tile that intersects some of its translates in Cantor sets,even though in the tiling it generates,it has only vertex and edge neighbors.This suggests that Cantor set intersection is a universal phenomenon among self-affine tiles.