Generic Function Finder

Genetic Function Finder by Aaron Golden Contents -What is GFF? (Genetic Function Finder) -How does GFF work? -How to use GFF -Limitations -Random Function Finder -FAQ (Frequently Asked Questions) -Comments What is GFF? (Genetic Function Finder) Genetic Function Finder is a program that searches for a function that will produce certain points on a two dimensional coordinate plain. For example, the function 'y = x' produces the points (1, 1), (2, 2), etc. Genetic Function Finder uses a survival of the fittest environment, to evolve the correct function by random mutations. The point of GFF isn't really to find the correct function, but to demonstrate a kind of evolution. How does GFF work? Genetic Function Finder starts by taking three points (given by the user) and generating ten random arithmetic strings. Then GFF evaluates each string and finds its value for each point. For example the string 'x+1' would yield '1' if 'x = 0', '2' if 'x = 1', '3' if 'x = 2'. GFF finds the difference between the results of each string, and the 'y' values for each point the user gave it. Here's an example: 1. The user gives the points: (1, 2) (2, 3) (3, 4) 2. GFF produces a string, S: 'x + x - 2' If 'x = 1' then 'S = 1 + 1 - 2 = 0' If 'x = 2' then 'S = 2 + 2 - 2 = 2' If 'x = 3' then 'S = 3 + 3 - 2 = 4' 3. GFF finds the difference between the results of the random string, and the real results. Random string yields: 0, 2, 4. Real results are: 2, 3, 4. (2 - 0) + (3 - 2) + (4 - 4) = 3 The total error of this string was '3'. 4. GFF produces nine more strings and finds the total error of each of them. 5. GFF then erases the strings with the largest five errors. (They die) 6. The best five strings from this generation are duplicated. (They reproduce) 7. The duplicate strings are mutated randomly to stimulate evolution. 8. The process is repeated, generally getting better and better results each generation until the correct string appears.