The Rise of Polynomials - Part I

This video shows a Polynomiograph (a visualization in approximation of zeros of polynomial equation) of Z Cubed minus 1 (Z^3 - 1) and a projected 3D extrapolation of regions according to their mathematical correlations to the roots. To learn more about this new and exciting subject please visit www.polynomiography.com

Category:

Education

Tags:

• Bahman
• Kalantari
• Polynomiography.com
• polynomials
• polynomial
• equations
• art
• math
• visualization
• 3D
• Adrian
• Sinclair
• Z-Cubed minus one
• Z^3-1
• fractals

[concordance11]

This is owesome!

[CogitoErgoCogitoSum]

you replied to your own video with a compliment?

[forceuser17]

Never before have I seen math presented in such a dramatic fashion.

[Sano22n]

ROFL THIS SHIT IS 2 INTENSE !!!! OMG 

[Sano22n]

@forceuser17 ROFL

[bryceguy72]

Music is way too dramatic.

[bryceguy72]

@CogitoErgoCogitoSum Consider the region of the complex plane from -2 to +2 on both axes. Take a point from this region (x,y) (that's 2 values) and iterate using Newton's root-finding algorithm for complex polynomials. In this animation the polynomial is Z^3-1=0 and the color is determined by which root the algorithm found (only three possible roots, so only three colors). that's the 3rd value. The height is derived from the number of iterations required to arrive at a root... 4th value.

[Dzotshen]

@CogitoErgoCogitoSum

pwesome

[tubolclorosis21]

i hate the sound but ty anyways :D

[CogitoErgoCogitoSum]

Im curious... what does this 3-d visualization represent? I didnt get your video details. z^3 -1 has one input (z) and one output. But you managed to graph 3-space (which requires three values)... (not to mention the color coding). What do the axes represent?