A Tool to track results of iterating multivariable complex functions
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Hello! I am doing work with iterating multivariable complex functions on the polydisk and thought it might help to be able to visualize the process. My plan was to generate a matrix of values by using a for loop to evaluate the function at the last coordinate, and then save the new coordinate in the next matrix entry, and then graphing the results I want by pulling consecutive terms out of the evaluation matrix.
I haven't done a lot with matlab in quite some time, and last time I used it I didn't do a whole lot of graphing. Ideally I'd like to be able to have a number of different plots, each one representing a different entry of the polydisk running in parallel so I can visualize each coordinate separately.
That's the idea. I have two questions; First, is there a better way to do this that I just don't know about? What I care about is the "end term behavior" of each coordinate of the function, so I don't necessarily need the short-term data (although having it wouldn't hurt), I just need the deep iterative data. Second I need a list of starting points. Ideally I'd like every hundredth of a point between -1 and 1 and between -i and i, which means something like 40,000 points in total. Is there an easy command to generate that list of complex values? I was thinking maybe something along the lines of the : operator in each dimension, but I didn't know if I can make 1 point by using two of those operators (I know I can make the real number list and then the imaginary number list, but I don't know if there's any nice way to combine the two to get all the complex numbers).
Thanks for the help.
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Accepted Answer
Walter Roberson
on 23 Nov 2015
coords = linspace(-1,1,200);
[P,Q] = ndgrid(coords,coords);
start_grid = complex(P,Q);
I do not understand about "deep iterative data", and I do not know what a "polydisk" is. I do not understand your visualization strategy as yet.
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