Fitness is defined simply as the number of 0s or 1s that match the model string. If you first draw a red Math stuff, then replace it and replace a black ball by a red one. The configuration continuously reproduces itself all the while emitting a "glider" towards the southeast corner of the rectangle.

With a mutation rate of say 0. A cell cannot infect itself so the only contagion can come from its neighbors. To run the program, hit the function key F9 Calculate Now.

This is used in all the spreadsheets below.

One can model increasing returns-type processes Math stuff a Polya's Urn model programmed on a spreadsheet. Right-click on the name and choose "Save Target As? This is the simplest type of genetic algorithm after the fashion of John Holland see his book Hidden Order.

You can change those initial endowments in row 6. Thus Polya's City is a circle or ring of neighborhoods. Everywhere else is a wasteland of "broke" neighborhoods as you see above. Do not touch the keyboard or click mouse until the iterations stop even if the life forms stabilize or vanish otherwise see instructions above under "Iteration Counters".

A cell is infected for only one period or iteration, and then has to be reinfected to be sick again. The following spreadsheet just introduces iteration counters. The key trick in any spreadsheet with circular references and iterations is the iteration counter. By thus synchronizing the counter with the spreadsheet, the counter will automatically reset itself to 1 at the end of each complete run.

The spreadsheet is set to run a fixed number of iterations and that number must be entered in the MaxIter box of the spreadsheet. Equilibrium Random Start Bead Game: The configuration continuously reproduces itself all the while emitting a "glider" towards the southeast corner of the rectangle.

When the user aborts a run at a smaller number of iterations e. Thus one can directly compare different mutation rates.

Eventually the red or black balls will dominate and drive out the others. To change the outcome, you need to change the dynamics. Fitness is defined simply as the number of 0s or 1s that match the model string.

The iteration counter internal to Excel runs in the lower left corner. The Game of Life. This is done by double-clicking on the Index cell the cell below the label and hitting Enter, one resets the Index value to 1. One can model increasing returns-type processes using a Polya's Urn model programmed on a spreadsheet.

When a location hits zero, it goes "broke. A cell can be infected by one of its four neighbors east, west, north, and south with a probability P. There is an initially random population of a fixed number of members 6 in this case that evolve using selection, mutation, and crossover.Cool Math has free online cool math lessons, cool math games and fun math activities.

Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too.

Math help since Math Goodies helps kids at all levels with interactive instruction and free resources. Get help online or offline. "Good Stuff" - Math Games, Materials, & Other Stuff Welcome. This page lists assorted resources not listed on the home page. Use any of the following for nonprofit purposes, but, please state the source and give credit to the author.

John Baez's Stuff I'm a mathematical physicist. I work at the math department at U. C. Riverside in California, and also at the Centre for Quantum Technologies in Singapore.

I'm working on network theory, information theory, and the Azimuth Project, which is a way for scientists, engineers and mathematicians to do something about the global ecological crisis.

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