Bitmaps

• Fractals: introduction
  • Barnsley’s Fern
  • Dragon curve
  • Sierpiński carpet
• Fractals related to the Mandelbrot set
  • Mandelbrot set, example 1, classical set: \(z_{n+1} = z_n^2 + c\)
  • Mandelbrot set, example 2: higher powers
  • Mandelbrot set, example 3: \(z_{n+1} = z_n^5 + \frac{c}{z_n}\)
  • Mandelbrot set, example 4: \(z_{n+1} = z_n^5 + \frac{c}{z_n^5}\)
  • Mandelbrot set, example 5, “Inverse Mandelbrot”
  • Mandelbrot set, example 6, “Marek Dragon Fractal”:
  • Mandelbrot set, example 7, “Burning Ship Fractal”
• Fractals related to the Julia set
  • Julia sets, example 1: Classical set
  • Julia sets, example 2: Glynn fractals
  • Julia sets, example 3: Spiral Septagon fractal
  • Julia sets, example 4: Reuleaux Triangle fractal
  • Julia sets, example 5: Phoenix Julia fractals
  • Julia sets, example 6: Cubic Julia fractals
  • Julia sets, example 7: Spiral Julia fractal (uses \(z_{n+1} = \tan(z_n^2 +c)\))
  • Julia sets, example 8: Julia set of \(\sin(z)\)
  • Julia sets, example 9: Julia09 fractals
  • Julia sets, example 10: Julia10 fractals
  • Julia sets, example 11: Julia11 fractals
• Newton Fractals
  • Newton, zeros of \(z^3-1\)
  • Newton, zeros of \(\cos(z)\)
  • Modified Newton (containing an error), zeros of \(z^3-1\)
  • Modified Newton (containing an error), not converging
  • Halley, zeros of \(z^3-1\)
  • Halley, zeros of \(\cos(z)\)
  • Modified Halley (containing an error), zeros of \(z^3-1\)
• Domain coloring
  • Domain coloring without contours: \(f(z) = (z^3-1)/z\)
  • Domain coloring with contours of the phase: \(f(z) = (z^3-1)/z\)
  • Domain coloring with contours of the modulus: \(f(z) = (z^3-1)/z\)
  • Domain coloring with contours of phase and modulus: \(f(z) = (z^3-1)/z\)
  • Domain coloring with contours of phase and modulus: \(f(z) = z^5 + z\)
  • Domain coloring with contours of phase and modulus: \(f(z) = (z^6-1)/(z^{12}+1)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = (z-0.5(1+i))/z^2\)
  • Domain coloring with contours of phase and modulus: \(f(z) = \exp(1/z)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = z \exp(1/z)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = \exp(1/z^2)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = \sin(z)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = z \sin(1/z)\)
  • Domain coloring with contours of phase and modulus: \(f(z) = \sin(z) / (z-i)^2\)
  • Domain coloring with contours of phase and modulus: \(f(z) = \tan(z)\)