Chaotic art

The work of a curious fellow

Chain on Cushion Dynamic Toadstool

.:Nature's Hidden Art - Images found in the mathematics of natural systems...

Visible Fractal Structure
Photo "Oak Tree in Winter" by Snemann

Nature provides some striking images, visible records of movement, like the fractal branching evident in the growth of an oak tree as it fills the space allotted to it.

The visible Art of nature though is not the whole story. The fluttering of an oak tree's leaf in the breeze does not leave a permanent record of that motion but just out of sight, one or two levels of abstraction below the visible, that motion creates its own Art. It turns out that the complicated motion of a fluttering leaf may be approximated by mathematical expressions. Applying appropriate imaging algorithms to these mathematical expressions we can create a portrait of the leaf's behavior. This same technique applies to all physical objects in motion, a bouncing ball, a satellite in orbit, ocean waves or whatever.

Mathematical models of more abstract systems are possible, population growth, the spread of disease, the life cycle of a rumor and so forth. The behavior of these systems also leads to striking images when properly displayed. In fact since the images arise from the mathematics describing the systems, we can generate images for systems that do not, as far as we know, exist in nature.

The images displayed in the galleries linked on this page are captured from actual moving objects like the fluttering oak leaf or from made-up systems that so far as we know exist only as mathematical expressions. The galleries are organized according to the particular algorithm used to extract the image from the mathematics of the systems. If you click on one of the small images, shown below, you will be transported to a small collection of images produced by the indicated algorithm. Clicking on the small images in each gallery will present a larger image and information on the mathematical system from which the image came. If you have the time and are so inclined, by following all the links in these pages you can get a pretty good understanding of the system dynamics. Otherwise just enjoy these crude sketches from natures portfolio. They are indeed crude. The computer cannot begin to capture the fine detail of the real image. The images below the navigation buttons are more examples of nature's hidden Art.

The "Complex Sets" and "Attractor Mists" collections of images were produced by Ross Hilbert's Fractal Science Kit. Click on the Fractal Science link for details on how to get that program. The "3D Attractor" images were produced by the Chaoscope program. Click on the Chaoscope link for details on how to get that program, which is an ongoing project created and maintained by Nicolas Desprez. The images in the remaining galleries were created with a program called "Order" that we wrote to help teach the mathematics of chaos. A limited version of Order is available on this site. Click on the link Order for a free copy of the industrial strength version. Just run the OSetup.exe program to install Order on your computer. You may need to agree to download and run the program, depending on your security settings.

High Strung
Complex Sets
Attractor Mists
Attractor Mists
3D Attractors
3D Attractors
Spectrum Intercept
Sea Creatures
Escape Time
River of Gold
Basins of Attraction