Saturday, February 25, 2012

a type of complex plot

I thought of this way to visualize a polynomial with a complex domain and complex range. This is the polynomial x^10-1 with the real and imaginary component of x between -1 and 1 and -1i and 1i respectively. To show the complex output of certain values of x, I colored the pixel as more red the bigger the real component and more green the bigger imaginary component. In computers red and green light mixed together make yellow so bright yellow is where both the real and imaginary component of the function output are 1. Black areas are where the function is closer to -1 in both the real and imaginary component.

 For reference where the function equals 0 will have a color of:

Better would be to use a 4 component color system like CMYK and have more C to be more positive real and more M to be more positive imaginary and Y and K for more negative real and imaginary which could be printed on most printers but what you would see on the computer screen would just be an approximation because the computer only uses 3 components. Then the most black parts would be where the equation equals 0.

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