Newton’s fractal (which Newton knew nothing about)

Summary by Krater

This video explains Newton's method for finding roots of polynomials and how applying it in the complex plane generates intricate fractal boundaries. It concludes that boundaries between root basins in Newton's fractal always share the same boundary set across all colors.

From the video

Answers: What is a Newton's fractal and why does it look so complicated?

• Newton's method
• Polynomial roots
• Newton's fractals
• Complex plane dynamics
• Holomorphic dynamics

What it concludes

• There is no analogous formula to solve polynomials of degree five or more using standard algebraic operations.
• The boundary of one color basin in Newton's fractal is identical to the boundary of any other color basin.
• Any smooth segment in Newton's fractal boundary is disallowed because smoothness implies touching only two colors.