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Strategies and Rubrics for Teaching Chaos and Complex Systems Theories as Elaborating, Self-Organizing, and Fractionating Evolutionary Systems. Fichter, Lynn S., Pyle, E.J., and Whitmeyer, S.J., 2010, Journal of Geoscience Education (in press). Elaborating Evolutionary Mechanisms.

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Strategies and Rubrics for Teaching Chaos and Complex Systems Theories as Elaborating, Self-Organizing, and Fractionating Evolutionary Systems

Fichter, Lynn S., Pyle, E.J., and Whitmeyer, S.J., 2010, Journal of Geoscience Education (in press)


Elaborating Evolutionary Mechanisms

The General Evolutionary Algorithm

1. Differentiate

The units of selection and the information carriers are different in each kind of system but the algorithm is the same . . .

2. Select

3. Amplify



Elaborating Evolution

Word Evolv

Genetic Algorithms


Elaborating Evolution

A genetic algorithm (GA) is a search technique used to find exact or approximate solutions to a problem.

In biological evolution the “solution” is measured as a fitness function, how well adapted the organism is to its environment.

Natural selection works on the organisms, eliminating those that are less fit, while allowing the more fit to live, and reproduce.

For example . . .


General Evolutionary Algorithm in Biology






Elaborating Evolution

WordEvolv is a genetic algorithm that demonstrates how efficient natural selection is. The procedure is . . .

Create a fitness function. For example, the phrase, “What is this phrase.” This is known as the target string.


1. Generate at random 20 strings of letters and spaces of the same length as the target string.

2. Pass the 20 strings through a selection filter, comparing each of the strings with the target string. Keep the one string closest to the target, discard (select out) all the other strings.

3. Reproduce the one surviving string 20 times, but mutate each at random (i.e. change one letter in each string from the initial).

4. Repeat process.


Elaborating Evolution

John Muir Trail

Can we evolve via natural selection (i.e. a genetic algorithm) an electronic “ant” that can learn to run a maze?


The John Muir Trail

The Trail

The trail itself is a series of black squares on a 32x32 white toroidal (ie, wraparound) grid. Each black square is numbered sequentially, from 1, directly next to the starting square, to 89, the ending square. The ant's task is to follow this trail and move across each square in sequence: That is, it does not get a score of 89 for waltzing across the board from square 0 directly to square 89. It must first visit each square in turn.


The John Muir Trail

Random Approach

UCLA experiment: the power, or lack thereof, of a random search.

  • 1 billion strings of genetic code were generated at random.
  • The best was only able to get to square 81 on the trail.

The John Muir Trail

Evolutionary Approach

Generate a series of electronic “ants” each with a genetic code created at random.


The John Muir Trail

The Ant gene consists of 512 bits of information, a series of 1's and 0's. The genetic makeup is changed each generation at some low frequency either by cross over—two individuals exchange part of their string of genes—or by mutation—one gene has its bit flipped from 1 to 0 or vice versa.


The John Muir Trail

The ants are simple state machines which can move along the trail and sense their immediate surroundings.

  • The ant stands on a single square and can face north, south, east, or west.
  • It is capable of sensing the state of the square directly in front of it.
  • In each time step, the ant must take one of four actions. It may turn left, turn right, move forward one step, or stand still.
  • The ant's score is the value of the highest square it was able to reach when a fixed amount of time has passed.

Learning to Run the John Muir Trail

1. The first generation of ants was given totally random genotypes—they were strings of ones and zeros selected by chance.

2. A population of 64 K, or 65,536, of these "random" ants was created.

3. In this first generation, it was common for ants not to move at all, or to move haphazardly, or to continue stubbornly in a single direction.

4. After each ant was scored, the top 1% was selected for reproduction in the next generation and copied to compose a full population


Learning to Run the John Muir Trail

5. During reproduction.

  • Mutate a small percent of the new ants at a low rate
  • Conduct crossovers at a certain small rate.



The John Muir Trail

Typical Run of an Ant Experiment as run by Patrick Brennan; note that an ant capable of running nearly the entire trail evolved in less than 200 generations.


Danny Hillis, 1991, 'Co-evolving Parasites Improve Simulated Evolution as an Optimization Procedure'

Ramps is a genetic algorithm evolving to reach a fitness peak at solving a mathematical problem - the ability to sort a random number list. Fitness is measured by the shortest number of steps evolved to solve the various problems present in the environment.

Antiramps is a genetic algorithm evolving to reach a fitness peak at creating test cases the Ramps can not solve well with the strategies evolved to date. That is, the most fit Antiramps are those which resist being sorted easily or well.


The Prisoner’s Dilemma and

Evolution of Cooperation