Title: Complex bases Post by: lkmitch on July 12, 2011, 04:15:51 PM 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.
Title: Re: Complex bases Post by: matsoljare on July 12, 2011, 10:26:57 PM And it just happens to resemble a very well known IFS fractal :evil1:
Title: Re: Complex bases Post by: DarkBeam on September 20, 2011, 11:52:21 PM Yes a dragon! :fiery: Rawr ;) |