Copyright Andrew French 2013.

Mathematicon: An exhibition of mathematically engineered images
Andy French. Winchester, UK
Mathematicon is a series of nineteen images grouped into four themes: Spherium, Harmonograph, Circularis,
Julia. Each theme corresponds to a bespoke software tool designed to enable an intuitive exploration of the
curves and surfaces associated with a particular set of mathematical relationships.
The concept of this exhibition is to illustrate the possibility of a harmonious synthesis between human and
machine, whereby the idea generation capability of the mind is hybridized with the extraordinary power of
precision calculation repetition offered by modern computers. The nature of the interface between these two
very different worlds is critical for humans to be empowered, rather than constrained, by technology.
Spherium (exhibits 01 to 12) is a three dimensional digital sculpturing tool which incorporates lighting,
transparency and texture mapping effects. A surface is created from a mathematical relationship between
spherical polar coordinates, that is range, azimuth and elevation. Other variants include Ammonites, where an
ellipse with periodic disturbances is extruded around a spiral.
A Harmonograph (exhibit 17) is a Victorian curiosity consisting of two or three coupled pendulums connected to
a sheet of paper and a pen. Particularly interesting traces can be obtained by setting the paper in a clockwise
circular motion and the pen in an anticlockwise sense. In the digital Harmonograph, the four control parameters
(amplitude ratio, phase, rotation frequency and damping) are set dynamically by a set of sliders reminiscent of
the graphic equalizers attached to the exterior of pre-iPod stereos. Unlike the mechanical version, the digital
Harmonograph generates the pen trace almost immediately. This enables the dependence upon control parameters to
be investigated dynamically.
Circularis (exhibit 16) is a computer program for curve stitching, that is the drawing of straight lines
between equally spaced points along a set of curves. In exhibit 16, the first epicycloids are drawn (Cardoid,
Nephroid, Epicycloid of Cremona).
Julia (exhibits 13,14,15,19) is a mechanism for the generation of surfaces formed from repeated transformations
of the Argand diagram, that is a two dimensional space metricated by real and imaginary number lines. These
infinitely detailed fractal forms, seemingly biological in nature, are determined from very simple equations.
The classic Mandelbrot, plus many variations, are a somewhat psychedelic conclusion to Mathematicon.
AF November 2013
Dr Andrew French is a physicist and he teaches mathematics at Winchester College.
He was formerly a 400m runner and a radar engineer.