Order and Complexity I

Edition 3/12

The Archimedes' Aquatics series is a set of 5 tessellating creatures, developed by the artist, based on squares and equilateral triangles which combine in many different ways.

The creatures themselves have a ‘valence’ or ‘charge’ where they either exceed or have a deficit in area for their basic geometry. The grey turtle has two protrusions and two subtractions and so is neutral (+2,-2 =0) , The cyan frog and purple swamp creature are positive (-1,+3 =+2), (-1,+2=+1) while the gold fish and green froglet are negative (-2,+1= -1), (-3,+1 =-2). So an interesting aspect of all the patterns is that the overall charge must equal 0 if there are to be no gaps or overlaps.

It is possible to make infinite spatial-animal equations from these condition - every frog can be balanced with 2 fish or one froglet, while any pattern of fish and swamp creatures will need an equal proportion of each. Only the turtle can tile on its own as it is has a neutral valence with 2 protrusions and 2 subtractions from its basic square.

These Archimedes Aquatics tiles have been used in a series of scroll artworks, the Order and Complexity series. Composed of arrangements of 5 creatures- a fish, a frog, a froglet, a swamp creature and a turtle - in different combinations, the design metamorphoses from regular patterns through a chaotic period to a self-similar pattern of a fractal structure and then back through chaos to a second regular pattern. This shift in the order of components is analogous to phase changes in materials, or chemicals bonding or the way a substance may crystallise in different ways at different energy levels or pressures.

The scrolls highlights the limits of raw human perception - we rely on our innate pattern processing ability to decide what is ordered and what is chaotic. The Order and Complexity scrolls makes visible this condition, and communicate the tantalising effect, known to any researcher - of sensing some form of hidden order in a data set and wondering how to unlock the secret.

This scroll, number I in the series, uses a combination of 4 creatures. The turtle, fish and swamp creature form starbursts at the top of the scroll, a pattern which gets disrupted by the arrival of the frog. In the centre of the panel, the 4 creatures resolve into a substitution tiling using the 4 creatures. Towards the lower third of the screen, the turtle and swamp creature become less common, finally resolving into a regular pattern of frogs and fish.