Complex bases

[lkmitch]

It's well known that Gaussian integers (complex numbers with integral real and imaginary parts) can be expressed using complex bases (e.g., the base -1+i).  This image shows one subset of integers that can be described in 16 bits or fewer using the base 1+i.  It's two layers: one colored by how many 1's in the representation (1+i uses the digits 0 and 1), the other corresponding to the size of the number, when taken as a regular binary number.

[matsoljare]

And it just happens to resemble a very well known IFS fractal

[DarkBeam]

Yes a dragon!  Rawr