Awesome mathematics: an image of the root of an Integer Polynomial on a complex plane

Dan Christensen found that all the roots of an Integer Polynomial whose number is not greater than 5 and whose coefficients are within the range of-4 to 4 are depicted on the same complex plane, you will see a spectacular picture. Each Gray Point in the figure represents a root of a quadratic polynomial, blue points represent the root of cubic polynomials, red represents the root of a cubic polynomial, and black represents the root of a cubic polynomial. The horizontal line represents the solid axis, where 0 and ± 1 have obvious holes. The vertical direction is the virtual axis, and each unit root also has clearly identifiable holes.

 

 
 
Inspired by the above experiments, Sam Derbyshire decided to draw a more general, higher-resolution polynomial complex root map. Consider that each coefficient is either 1 or-1 of all 24 polynomials, they will generate a total of 24*2 ^ 24 -- about equal to 0.4 billion -- a root. He asked Mathematica to run for four days and four nights to figure out the location of all these roots and get about 5 GB of data. Finally, he used a Java program to plot the distribution of these roots on the complex plane:

 
 
 
Below is a local zoom-in diagram:

 

 
 
 
This is a local zoom-in Image located near 1:

 

 
 
 
This is a local zoom-in near 4/5:

 

 
 
 
This is a partial zoom-in near (4/5) I:

 

 
 
 
The most beautiful part is the local zoom-in image near (1/2) * exp (I/5:

 

 
 

 

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