Images

Animations

The following link gives the abstract to an article describing these animations appearing in the SIGGRAPH Educators Program Proceedings, 2004:
http://www.siggraph.org/s2004/conference/edu/animation.php?=conference.

The following link will provide new animations in the future:
http://www.cs.rutgers.edu/~kalantar/Animation.

Dance

This is polynomiography animation with a fourth degree polynomial.

Sensitivity

This is polynomiography animation with the polynomial (x-1)(x-2)(x-3)(x-4)(x-5)(x-6) showing the sensitivity of the roots to changes in the coefficient of x^6 as it is decreased, some becoming complex numbers.

Polynomiography of polynomials in a problem of Knuth

This is polynomiography animation with the polynomial p(x)=summation of a_k * (n choose k) z^k (1-z)^{n-k} where the vector a=(a_0, ..., a_n) is a point in (n+1)-dimensional hypercube. In this example we have n=5 and we take a range from (0,1,0,1,0,1) to (1,0,1,0,1,0). This amounts to going from one corner of the 6D hypercube to the opposite corner.

Rotation

This is polynomiography animation of the roots of x^4-1 under rotation of the roots, induced by the change of variable x with e^it x, where t goes from 0 to pi/2. (e^it=cos t+ i sin t)

Zoom

This is a polynomiography animation with zooming.

A Problem of the Monthly

This is a polynomiography animation with x^m(x^4-1) for different values of m.

Playing with fourth root of unity

This is polynomiography animation corresponding to approximation of roots of (x^4-1) under different iteration functions.

Spiral

Billiard

Voronoi Regions - Roots of Unity (x^4-1)

This is a polynomiography animation with basins of attraction of (x^n-1) for different iteration functions.

Voronoi Regions - Random Points

This is a polynomiography animation with basins of attraction of a polynomial under different iteration functions.