A Simple Procedure to Generate Curves and Surfaces

Alan Sutcliffe
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 217–224


A method is presented of synthesizing irregular but smooth curves for display at screen resolutions of the order of 1200 by 1200 pixels. The method uses the addition of differences of differences of differences in one coordinate for unit increments in the other coordinate. The curves are extended laterally by simple shading to produce the appearance of smooth forms in 3-dimensions. Drawing in the XOR mode gives unexpected benefits in this context. There is a brief note on the procedural approach to composition compared with conventional methods. A final note describes the operation of XOR applied to grey-scales and colours.