logistic function can produce chaos although our program has well defined underlying behaviorthe output seems unpredictable an interesting property of chaotic functions is that very small differences in the initial value can lead to large differences in the result as the formula is repeatedly applied you can see this in the chaos program by entering numbers that differ by only small amount here is the output from modified program that shows the results for initial values of and side by sideinput with very similar starting valuesthe outputs stay similar for few iterationsbut then differ markedly by about the fifth iterationthere no longer seems to be any relationship between the two models these two features of our chaos programapparent unpredictability and extreme sensitivity to initial valuesare the hallmarks of chaotic behavior chaos has important implications for computer science it turns out that many phenomena in the real world that we might like to model and predict with our computers exhibit just this kind of chaotic behavior you may have heard of the so-called butterfly effect computer models that are used to simulate and predict weather patterns are so sensitive that the effect of single butterfly flapping its wings in new jersey might make the difference of whether or not rain is predicted in peoria it' very possible that even with perfect computer modelingwe might never be able to measure existing weather conditions accurately enough to predict weather more than few days in advance the measurements simply can' be precise enough to make the predictions accurate over longer time frame as you can seethis small program has valuable lesson to teach users of computers as amazing as computers arethe results that they give us are only as useful as the mathematical models on which the programs are based computers can give incorrect results because of errors in programsbut even correct programs may produce erroneous results if the models are wrong or the initial inputs are not accurate enough