Dimensions of Intersections, Exercise 4 Answers

Denote the Sierpinski gasket by S and the product of two Cantor middle thirds sets by P.

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

dim(S ∩ P) = dim(S) + dim(P) - E

For E = 2 this becomes

dim(S ∩ P) = Log(3)/Log(2) + Log(4)/Log(3) - 2 ≈ 0.847

For E = 3 this becomes

dim(S ∩ P) = Log(3)/Log(2) + Log(4)/Log(3) - 3 ≈ -0.153

Return to Dimension Algebra Exercises.