View Littlewood Dragons in HD on the Vimeo site.
This video shows all the Littlewood polynomials of degree 25 with a positive constant term — that is, polynomials of the form:
L(z) = 1 ± z ± z2 ± z3 ... ± z25
— evaluated at a point that moves around in the complex plane. The inset shows the location of the point against a backdrop of the set of roots, within a disk of radius 0.8, of the same polynomials.
The small white cross in the centre of the main image marks zero in the complex plane for the evaluations. As various families of polynomials (those sharing the same low-order coefficients, indicated by the colour of the points) sweep over zero, the same polynomials, and some very similar geometry, can be seen in the roots set.
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