Compiled and graphics by Paul Bourke

6 July 1998

I will give you an example of a function that is useful
developed from measure ideas. Suppose we have a measure:
and another measure:
and we try to get a function where both measures are true in the limit domain 0>s>2:
g(x,y,s) = y / (x^s + y^(2 * (s - 1)))^(1/s) f^s + g^(2 * (s - 1)) = 1 Such a function has some simplicity and theoretical worth and can be understood by almost everyone as a demonstration of what measures mean geometrically. If we change it into an iteration function:
y = x / (x^s + y^(2 * (s - 1)))^(1/s) + a(i) and let:
we, then, have a visualization of a measure function! It is a connected function that is very probably self-affine and very near d = 1. |