Before revision: Finite automata working bitwise on the local coordinates of points in the plane are constructed and shown to lead to self-affine surfaces ('patchwork quilts') under general circumstances. We prove that these models give rise to a roughness exponent  that shapes the resulting spatial patterns : Larger values of the exponent lead to coarser surfaces .
After revision: Finite automata working bitwise on the local coordinates of points in the plane are constructed and shown to lead to self-affine surfaces ('patchwork quilts') are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all bitwise operations on a finite alphabet which are not governed by chance. It is shown that these models give rise to a roughness exponent that shapes the resulting spatial patterns : Larger values of the exponent lead to coarser surfaces .