Dimensions of Intersections, Exercise 5 Answers

Denote the Cantor middle thirds set by C 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(C ∩ P) = dim(C) + dim(P) - E

For E = 2 this becomes

dim(C ∩ P) = Log(2)/Log(3) + Log(4)/Log(3) - 2 ≈ -0.107

For E = 3 this becomes

dim(C ∩ P) = Log(2)/Log(3) + Log(4)/Log(3) - 3 ≈ -1.107

Return to Dimension Algebra Exercises.