Extensions

The digital art at joebartholomew.com is grouped by project. Many of these projects share a common purpose — to extend a graphics system in some new way and thereby provide a tool for creating new imagery. The Rectangles and Spirals project extends features of the golden rectangle to other rectangles by generalizing the golden ratio formula and the Fibonacci number sequence. The Small Programs and Plane Symmetry Groups projects relate to plane symmetry or wallpaper groups, but differ in ways that disqualify them from, while extending the mathematical form.

The Coprimes and Greatest Common Divisor (GCD) projects plot the GCD of integers as colored cells within a grid. Patterns are generated by extending the integers provided to the GCD calculation beyond the grid column and row numbers. These numbers figure in a pair of formulas to generate different GCDs.

I based the Perspectives project on a simple two-point perspective drawing function. Instead of using the tool to create visually accurate perspective drawings I mix several viewpoints within the same drawings.

The Cubes and Cabtaxi Fleet project is based on the recreational math idea of taxicab and cabtaxi numbers. It suggests possibilities for representing the numbers in sculpture.

Here's my latest Small Programs drawing, "Apse". The apse, a frequently vaulted recess at the sanctuary end, may extend the exterior of a church.