Awesome math: The image of the root of the polynomial of integral coefficients on the complex plane

Dan Christensen found that all the roots of the coefficients polynomial in the range of 4 to 4, which are not more than 5, are depicted on the same complex plane, and you will see an unusually spectacular picture. Each gray point in the graph represents a root of a two polynomial, the blue point represents the root of the three polynomial, the red represents the root of the four-time polynomial, and the black represents the root of the five-time polynomial. Horizontal lines represent axes, 0 and ±1 where there is a clear void; the vertical direction is the virtual axis, and each unit root has a distinctly recognizable void.

Inspired by the above experiments, Sam Derbyshire decided to draw a more general, more high-resolution polynomial complex root diagram. Considering that each coefficient is either 1 or 1 of the total 24-time polynomial, they will produce 24*2^24--approximately equal to 400 million--a root. He had Mathematica run for four days and four nights to figure out where all these roots were, and got about 5 g of data. Finally, he uses a Java program to draw the maps of these roots on the complex plane, and miracles occur:

Here is a partial enlargement:

This is a local enlarged map located near 1:

This is a local enlarged map located near 4/5:

This is located near (4/5) I of the local amplification map:

The most beautiful place is the 1/2 (I/5) *exp near the local enlarged map:

See more: http://math.ucr.edu/home/baez/roots/