Chapter 5 Notes > Section 4 > Page 935 > Note (b)

	Notes for: Two Dimensions and Beyond | Substitution Systems and Fractals Space-filling curves One can conveniently scan a finite 2D grid just by going along each successive row in turn. One can scan a quadrant of an infinite grid using the σ function on page 1127, or one can scan a whole grid by for example going in a square spiral that at step t reaches position (-1)^#({1, -1}(Abs[#^2 - t] - #) + #^2 - t- Mod[#, 2])/2 &[Round[Sqrt[t]]] PAGE IMAGE RELATED LINKS Pages related to this note: 192 All notes on this page: The Mandelbrot set Neighbor-dependent [2D] substitution systems Space-filling curves Implementation [of network systems] Rule structure [for network systems] [Systems based on] undirected networks All notes for this section Downloadable programs for this page Downloadable images Search Forum for this page Post a comment NKS | Online FAQs

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