The equations/algorithms of that define attractors such as these:
With given parameters and number of iterations output a set of positions, the size of the set is the same as the number of iterations.
Can attractors like these, or their $2D$ versions be rearranged to simulate an infinite number of iterations?
The new equation/algorithm would take the parameters and additionally $X, Y$ and, if applicable, $Z$ coordinates, but no number of iterations.
Returning a non-negative real number instead of a set of positions, this number would represent the distance between the specified position and the nearest point in the attractor.