Dimensions of Intersections, Exercise 2 Answers

Denote the Sierpinski gasket by S and the Cantor set by C.

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

dim(S ∩ C) = dim(S) + dim(C) - E

For E = 2 this becomes

dim(S ∩ C) = Log(3)/Log(2) + Log(2)/Log(3) - 2 ≈ 0.261

For E = 3 this becomes

dim(S ∩ C) = Log(3)/Log(2) + Log(2)/Log(3) - 3 ≈ -0.784

Return to Dimension Algebra Exercises.