Using Numbers Series for Morphing

Artists have been traditionally concerned with expressing simple ideas or feelings using complex visual forms and, inversely, with understanding how complex realities can be represented by and express simple, abstract rules. Our goal is to explore and classify the range of visual forms that ?minimal? abstract models may give rise to. We have therefore defined a framework that integrates an abstract model or rule, together with an expression function that translates model results to structural elements or properties of a visual form. Number series appear to be good candidates for this type of experiment, because they are simple (the whole series is usually represented with a single simple mathematical expression), inflexible (once started, it cannot be changed) and infinite (it never ends). Expression functions on the other hand may be arbitrary and subjective, and are chosen by an artist at will. Our case study is based on the well-known Fibonacci series and shows that, by constraining some aspect of the visual form, an expression function may translate the number series to a complex visual form confined within a predefined 2-D area. The technique is applied to morphing of polygons using Fibonacci numbers as coordinates of control points. Three morphing variants are investigated and the wealth of resulting visual structures is demonstrated on a set of examples. Finally, the perspectives of the approach for visual form description are briefly outlined.