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Fractal Color Patterns

Published on August 5, 2025 • 1,756 views • 2:11 duration

Dive deep into the mesmerizing world of fractal mathematics through this stunning visual journey. Watch as complex mathematical equations transform into breathtaking patterns of color and form. This video showcases various fractal types including Mandelbrot sets, Julia sets, and custom algorithmic patterns, each rendered with vibrant color palettes that shift and evolve throughout the visualization.

Active Equations

Mandelbrot Set

z_n+1 = z_n² + c

Where c is a complex constant and z₀ = 0

Julia Set

z_n+1 = z_n² + c

Current c = -0.7269 + 0.1889i

Escape Condition

|z_n| > 2

Point escapes to infinity when magnitude exceeds 2

Newton's Method

z_n+1 = z_n - f(z_n)/f'(z_n)

For finding roots of f(z) = z³ - 1

Color Mapping

color = iterations / max_iterations

RGB interpolation based on iteration count

Zoom Transform

z' = (z - center) × zoom + center

Current zoom level: 2.547 × 10¹²