Algebraic Fractals

From Mandelbrot set to higher dimensions

• Dynamical systems in complex plane
  • Quadratic equation, complex quadratic polynomial, complex dynamics
  • Julia set, Fatou dust, Douady rabbit, Herman ring, Siegel disc
  • Gaston Julia, Pierre Fatou, Adrien Douady, Carl Siegel
  • Mandelbrot set, Benoît Mandelbrot, John H. Hubbard
  • Tricorn, multibrot set, Misiurewicz point, Burning ship
  • Plotting algorithms, orbit traps, domain coloring, biomorphs, Buddhabrot
• Numerical systems
  • Root finding, Newton fractal
• Spatial fractals
  • Hypercomplex numbers, quaternions
  • William Rowan Hamilton, Alan Norton
  • Mandelbox, Mandelbulb, Daniel White

Discussion

• Real, Irrational, Imaginary (World of Mathematics)
• Clouds Are Not Spheres – The Life and Work of a Maverick Mathematician
• Fractals and the Art of Roughness (Benoît Mandelbrot)
• Benoît Mandelbrot, The Father of Fractals
• The Unravelling of the Real 3D Mandelbulb (Daniel White)
• Mandelbulb.com: Educational and Informational Site about 3D Fractals

Assignment

Multidimensional fractals

Fractal Domains – Fractal Explorer – Fractal Forge – Fractal Science Kit – Fractint/Winfract – Fractorama – Fractview – Fraqtive – Gnofract 4D – Kokos Fractals – Newton Fractal Viewer – Perceptron – QSFract – Slatcarf – Ultra Fractal – WinCIG – XaoS

Amazing Boxplorer – ChaosPro – Fractal Lab – Fragmentarium – Incendia – Mandelbulb 3d – Mandelbulber – Quat – Quatern – Quaternion Julia Navigator – Synthclipse

 

Next topic

Chaotic fractals  ▸