Instructions: A click anywhere in the crescent-shaped complex region will take you to a page with images, a movie and a specific description. Each grid square leads to a different page.
You may prefer to browse the different patterns by starting with my extension of Pearson's classification of the types of emergent behaviours. I also have special pages for the U-skate world and certain other very exotic patterns, and a Gray-Scott nomenclature glossary.
This web page serves several purposes:
This work led to new discoveries and scientific investigation described below.
What Is It?
All of the images and animations were created by a computer calculation using the formula (two equations) shown below. In Roy Williams' words, it is a "relatively simple parabolic partial differential equation". Details are below; the essence of it is that it simulates the interaction of two chemicals that diffuse, react, and are replenished at specific rates given by some numerical quantities. By varying these numerical quantities we obtain many different patterns and types of behavior.
The patterns created by this equation, and other very similar equations, seem to closely resemble many patterns seen in living things. Such connections have been suggested by:
and many more in more recent years. Beginning with Lee et al. [7] and Pearson [8] the field broadened, greatly facilitated by computer simulation.
Some of the colour maps I tried
In his original 1994 exhibit3, Roy Williams presented grayscale images for many pairs of k and F, each showing a "histogram-equalised view of the U component". He suggested that the images, after modification by "a little playing with the colour map" would be "quite attractive as gift-wrapping". My images, like Williams', meet their own edges seamlessly, so they would look good if you used them as wallpaper on your computer monitor, for example.
The organic appearance and great diversity of patterns makes Gray-Scott patterns ideal for purely artistic applications, such as my own screen saver:
The Xmorphia PDE5 screen saver
Even for fairly non-artistic purposes such as a scientific publication, much attention should be given to the visual presentation of the simulation data.
Another 4 trial colour maps
For this website, I wanted to express more than one dimension of information (specifically: u and ∂u/∂t) and I wanted the colour mapping to be the same everywhere in the system, so that any two images could be compared directly with the knowledge that identical colours always represent identical values of u and ∂u/∂t. This prevented the approach of using "histogram equalization" or anything that changes the mapping from data value to colour.