My colleague Richard Pink had the idea of illustrating the matrix I had found with F. Jouve and D. Zywina, whose characteristic polynomial has Galois group *W(E _{8})*, by plotting it on a grid with colors to indicate the size of the coefficients. This representation was then constructed by Leopold Talirz using Matlab, with the following result:

The square grid represents the matrix graphically, and the scale for colors is indicated on the right. I think this is an intriguing picture. Can anyone suggest an explanation for its structure? In fact, since the matrix arises by a product

it would actually probably be even more interesting to show the *evolution* of the matrix from the identity as more terms are added in the product (and even to continue beyond this matrix in a random walk, as this the motivation for the construction…). If this leads to a nice result, I’ll post it later…

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