Dimensions of Intersections, Exercise 6 Answers

Denote the Sierpinski tetrahedron by T and the gasket by G.

Recall the intersection formula: for almost all placements of T and G in E-dimensional space,

dim(T ∩ G) = dim(T) + dim(G) - E

For E = 3 this becomes

dim(T ∩ G) = Log(4)/Log(2) + Log(3)/Log(2) - 3 = Log(3)/Log(2) - 1 ≈ 0.58496.

Return to Dimension Algebra Exercises.