Animations
-
Rise
of Polynomials on YouTube
See the book ``Polynomial Root-Finding and Polynomiography'' for
explanation.
- 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.
