I edited my original post and changed some of the ks to k_1, k_2, and k_3 and also raised the nested sums to powers of k and found that if I added one more layer of nested sums I could produce self similarity for all layers.
I also saw the formula in the link from Wolfram, and I'm confused as to what
means.
I also saw the formula in the link from Wolfram, and I'm confused as to what
means.

