Zeros of Orthogonal Polynomials on the Sierpinski Gasket

How many zeros do the Orthogonal Polynomials have?

Degree 2 Antisymmetric Sobolev Orthogonal Polynomial

Degree 2 Antisymmetric Sobolev Orthogonal Polynomial

Bottom Edge Zeros of Sobolev and Legendre Polynomials
Total Edge Zeros of Sobolev and Legendre Polynomials
Side Edge Zeros of Sobolev and Legendre Polynomials

Edge Zeros of Sobolev and Legendre Polynomials

Notice that some polynomials have more than \(3n + 3\) zeros...