Dimensions of Intersections, Exercise 1 Answers

Denote the Sierpinski gasket by S and the Line segment by L.

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

dim(S ∩ L) = dim(S) + dim(L) - E

For E = 2 this becomes

dim(S ∩ L) = Log(3)/Log(2) + 1 - 2 ≈ 0.585

For E = 3 this becomes

dim(S ∩ L) = Log(3)/Log(2) + 1 - 3 ≈ -0.415

Return to Dimension Algebra Exercises.