Dimensions of Intersections, Exercise 7 Answers

Denote the Sierpinski tetrahedron by T and the Cantor set by C.

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

dim(T ∩ C) = dim(T) + dim(C) - E

For E = 3 this becomes

dim(T ∩ C) = Log(4)/Log(2) + Log(2)/Log(3) - 3 = Log(2)/Log(3) - 1 ≈ -0.36907.

Return to Dimension Algebra Exercises.