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CALResCo Images Section

Cell Image These pages show examples of the sorts of pictures generated within the complexity sciences. Many of these pictures are artforms in their own right and this association has led to a merging of the disciplines of the arts, sciences and mathematics within the complex systems field. The visualisation of research simulations by computer graphics is one of the main methods we have of investigating emergent phenomena. To navigate through the pages in turn press the Next button, or to select a particular page directly use the links at the bottom of the page. Press First to return to this page or Back for the previous page. If you are more artistically inclined you may wish also (or instead) to visit our Complex Art Exhibition Exhibition of traditional paintings.

This first set of images are Fractals generated using the FRACTINT program which is available free from many sources. Many forms of fractal are possible, the current V20 DOS program lists 106 basic types, each with almost infinite choice of settings. The space of possible fractals is so vast that only a few have ever been found.

Mandelbrot Image Julia Spiral Image Julia Cross Image Saturn Rings Attractor Quatjul Trilobite Image Lyapunov Image Newton Roots Image Planet Image

In order, they are a) A standard Mandelbrot set, b) A Julia Spiral closeup, c) Candles - Julia cross, d) Satrings - Rossler3D attractor looking like Saturn's rings, e) Trilobite - Quatjul discovery of a fossil, f) Lyapun2 - Lyapunov 2D bifurcation type, g) Newton7 - fractal roots of x to power 6, h) Planet - Spherical transform of a plasma type fractal

Symmetrical Icons are a fractal type that has many correspondences with traditional art, particularly religious and meditational forms. Structure arises by plotting chaotic dots and the image appears as if by magic.

Triangular Image Square  Image Pentangle Image Circular Image

IconTri2, IconSqr, IconPent and IconWhel. Icon type fractals of symmetries a) 3, b) 4, c) 5, and d) 29 sides

The 4 below are also icons and represent the various forms of attractor that result from small changes to one of the parameters. This sensitivity to initial conditions is crucial in Chaotic attractors of this type.

Disjoint Attractor Image Linked Attractor Image Solid Attractor Image Zoomed Attractor Image

Mind6, Mind8, Minda and Mindzom6. Lambda values of a) 1.794, b) 1.814, c) 1.894 and d) a zoom of the structure of one disjoint element

Cellular automata (finite state machines) are lattices of independently behaving cells, here in 1 or 2 dimensions. Each cell only pays attention to its immediate surroundings, the overall pattern that we see is emergent and not programmed.

Ordered CA Image Static  CA Image 2D Ant City 2D Mite Image

a) CAr51r1 - Structured 1D CA, forever changing, b) CAr61r9 - 1D CA that settles to repeat cyclically, c) Ant City - 2D Growing population, d) Mite7 - 2D Geometric lifestyle of a artificial mite.

Most of the above images can be generated for yourself in high resolution, using the parameter file option from FRACTINT. Some of these are generated by using par files made generally available by other people. The necessary parameters can be downloaded from here PARMFILE. This contains the author credits for all these pictures along with their original source locations (if any).

The following images are from the Fractal Vision system (book and program by Dick Oliver, pub SAMS) which iterates a fractal template (IFS) to build a recognisable image from small very simple copies of itself. This is the opposite of fractal compression and gives emergent patterns from a seed, usually consisting of just a few straight lines..

Cherry Tree Image Galaxy Image Hen Image Koch  Image

a) Flowering cherry tree, b) A spiral galaxy, c) Hen sat on a nest, d) Koch snowflake

Complex mappings - order from chaos, use simple formulae iterated over and over to produce the visible structure. Boolean nets self-organise themselves dynamically by having logic gates connected to each other at random, the system settles down over time into a stable structure.

Order from Chaos Image Chirikov Map Image Bifurcation Map Image Boolean Network Image

a) Simple 3 point shift pattern,, b) Chirikov Map chaotic pattern, c) Logistic map showing bifurcation, d) Boolean NAND network self organisation

Artificial Life systems show evolution in action with genetic mutation, sexual crossover and fitness selection . They use collections of agents (entities) that interact and develop emergent behaviours, similar to those we find in real life.

Competing Ants Image Cyclic Food Chain Image Co-Evolution Image Flocking Birds Image Evolution Image Evolving Mice Image Biomorph Image Quilt Image

a) Ant trails for competing species, b) Cyclic food chain of 15 species, c) Coevolution of herbivores and plants, d) Flocking of birds, e) Semi-totalistic automata evolution, f) Mice evolving to locate food, g) A Biomorph moth, h) Space covering with symmetrical icons

Software is freely available for most of these tasks. See the various FAQs for details.

Images Page 2 | Page 3 | Page 4 | Page 5a | Page 5b | Page 6

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Page Version 4.83 March 2005 (original December 1996)