**Everything you see is made of smaller things with the same shape.** +Anton Sherwood created this striking image by writing out complex numbers in base –1+i and coloring the plane according to the 'digits' of these numbers. The fractal curve you see all over here is called the

**twindragon**.

In 1964, S. I. Khelmenik wrote a paper in the Russian journal

*Questions of Radio Electronics* in which he showed that every complex number can be uniquely expressed as a string of bits with a decimal point in it, like

1011001.1101010101000000101001100111101011000010101...

if we work in base –1+i. This was rediscovered by Walter F. Penney in 1965, later by other people, and popularized by Donald Knuth in vol. 2 of

*The Art of Computer Programming*. For more on these see:

http://en.wikipedia.org/wiki/Complex_base_systems+Anton Sherwood has a great page of mathematical images, from which I took this picture:

http://bendwavy.org/doodle/