Bitmaps# Fractals: introduction Sierpiński carpet Dragon curve Barnsley’s Fern Fractals related to the Mandelbrot set Classical Mandelbrot set Mandelbrot set at higher powers Mandelbrot 6 Mandelbrot 7 Inverse Mandelbrot Marek Dragon Fractal Burning Ship Fractal Fractals related to the Julia set Classical Julia set Glynn fractals Spiral Septagon fractal Reuleaux Triangle fractal Phoenix Julia fractals Cubic Julia fractals Spiral Julia fractal (uses \(z_{n+1} = \tan(z_n^2 +c)\)) Julia set of \(\sin(z)\) Julia09 fractals Julia10 fractals 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 options 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: Examples part 1 Domain coloring: \(f(z) = (z^6-1)/(z^{12}+1)\) Domain coloring: \(f(z) = \exp(1/z)\) Domain coloring: \(f(z) = \exp(1/z^2)\) Domain coloring: \(f(z) = z \sin(1/z)\) Domain coloring: \(f(z) = \sin(z) / (z-i)^2\)