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Chaos and Complexity Computer Programs
If the program will not load, Go To: Start, Shutdown, "Close all programs and logon as new user." A new logon screen with "geolstud" will appear. Just click "OK" and you will be logged on to the server with the programs. In a few cases there are also available experiments for the programs taken from a GenSci 104 course in "Artificial Life, Chaos, and Complexity." Fractals in the Mandelbrot Set
When a figure is fractal it means that no matter how many times you enlarge the image, rich detail continues to emerge. The best example is the Mandelbrot set. This fractal scaling is the way nature is organized, and when trying to describe a part of nature the problem is deciding at what scale to observe and describe, back at a distance capturing the big picture, or up close capturing the subtleties. There are a few ways to experience it. Go there and try it.> Mandelbrot Set - A basic description > Exercises for the Mandelbrot Set in the Miller, Room 224 computer lab. > Link 1 - a page of Mandelbrot images, with some links to explanations of the set. Further links about fractals in general: link 1, link 2 , link 3 , link 4 . The Chaos Game and the Serpinski Triangle. This is a web based computer game that helps gain understanding about fractal geometry. > Web Link to the Chaos Game > Explanation and experiment. X-next
> 'X-next' - the behavior of this logistic equation is one definition of chaos. This link is a description of how the equation works.> Experiments with X-next. Some things to try. Cellular Automata
Life3000' - the cellular automata program we used to review the homework.> CA link. A brief description of what cellular automata are and how they work. > A web version of a CA is here. This site also has CA programs you can download to your own computer. > Experiments. 'Life' programs are a lot of fun to just play around with, but sometimes we need a little more systematic introduction. Try this set of experiments. » Cellular Automata Experiment » CA Experimental Record Pages 'Life' - another cellular automata; the class demonstrations ('Classifying Artificial Life Files From the Complexity Lab') were drawn from the 'File: Open' pull down menu. Attractors
The concept of attractors is extremely important in our discussions, and we use it many ways. It is important to become familiar with the various ways attractors exist, and are expressed.> Some Experiments to run using the several different programs listed below. > 'X-next' - we used the chaos equation to initially review attractors. > 'Galaxy' - we used this simulation of stars orbiting around each other to study limit cycle and strange (complex) attractors > 'Lorenz' - an example of a complex attractor. Genetic Algorithms
Genetic algorithms (GA) create electronic "bugs" and place them in an electronic environment where they can interact and evolve. These look similar to computer games, but differ in a fundamental way. In computer games all the actions are preprogrammed. In a GA the "bugs" can evolve and change their behaviors, sometimes in unpredictable ways.'MFBoids' is a neat program that simulates bird flocking behavior. We did not use this program in class, but a web version is here. > Also at the end of the Experiment for CA is an experiment for Boids. All the programs I used in class are available on the Geology Computer Lab computers, Miller 224 and you are welcome to play with them. Click on the 'Alife' icon on the desktop and double click any of the program icons to open the program. Chaos Theory (the X-next equation) is a branch of mathematics. It is closely allied with Complexity Theory (or the theory of Complex Systems), and Artificial Life (Alife) studies. All these branches of mathematics try to understand how complex systems behave. Complex systems include just about everything that is interesting in the universe, living systems, star systems, economies, political systems, a beating heart, an ant colony, the human brain, etc. Any open system that is regulated by positive and negative feedback and capable of evolving. Obviously the subject is much bigger than what we explored in class. But if this subject interests you come talk with me. I may be able to suggest some places to explore.  Return to Bio/Geo 350 Course Page, Invertebrate Paleontology: The History of Life on Earth
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