Patent ID: 8520004

Claim:
A computer-implemented method for generating curves resembling labyrinths and maze-like patterns, the method comprising: a) initializing by a computer curve evolution parameters and a curve network, wherein the curve network comprises a curve embedded in a two-dimensional non-Euclidean evolution space, wherein the curve comprises a linearly ordered set of sample points in the evolution space, and wherein the curve evolution parameters comprise real-valued functions defined on the evolution space; b) evolving by the computer the curve using an iterative process, wherein the curve evolves in accordance with the curve evolution parameters during the iterative process to produce an evolved curve having an increased geometric complexity; and c) rendering by the computer the evolved curve and displaying on a display the evolved curve; wherein each iteration of the iterative process comprises: i) resampling the curve to increase the uniformity of spacing between adjacent point samples of the curve; and ii) spatially modulating the sample points of the curve by the curve evolution parameters, wherein the spatial modulation comprises computing, for each of the sample points, a displacement calculated in part by evaluating at each of the sample points a function defined on the evolution space; wherein computing the displacement comprises calculating distances between each of the sample points and neighboring points using a surface distance metric that estimates a geodesic distance metric in the two-dimensional non-Euclidean evolution space.