Chapter 10: Processes of Perception and Analysis

Section 11: Traditional Mathematics and Mathematical Formulas

Complex powers [of numbers]

The pictures below show successive powers of complex numbers z with digits extracted according to

(2 d[Re[#], w] + d[Im[#], w]) & [zt]

d[x_, w_] := If[x < 0, 1 - d[-x, w], IntegerDigits[x, 2, w]]

Non-trivial cases of complex number multiplication never correspond to local cellular automaton operations. (Compare page 933.)

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]