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Viscomp I

Viscomp I. c2-2011. Entrega TP1 ?. Fractales y mapeo del espacio. El conjunto de Mandelbrot : conjunto de valores complejos ( z ). Fractales y mapeo del espacio. Fractal de Mandelbrot Zr i = Zr i-1 2 + Z 0 Converge cuando el modulo es < 2 ComplexNumber z0 = new ComplexNumber(r,i);

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Viscomp I

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  1. Viscomp I c2-2011

  2. Entrega TP1 ?

  3. Fractales y mapeo del espacio • El conjunto de Mandelbrot : conjunto de valores complejos (z).

  4. Fractales y mapeo del espacio Fractal de Mandelbrot Zri = Zri-12 + Z0 • Converge cuando el modulo es < 2 ComplexNumber z0 = new ComplexNumber(r,i); ComplexNumber zn = new ComplexNumber(0,0); double modulo = zn.module(); while ((count<256) && ((modulo)<2)) { zn = ComplexNumber.add ( ComplexNumber.square(zn), z0); modulo = zn.module(); count++; } return (count); } /// Esta es la variable que vamos a usar para colorear

  5. Cómo dibujo en pantalla ? • Fractal determinado entre • Zr (reales ) : -1.5 < zr < 0.5 • Zi (imaginario : -1 < zi < 1 • Pantalla

  6. Fractales y mapeo del espacio • Dado px y py ,mapear a espacio complejo int w = Buffer.Width; int h = Buffer.Height; rMax = 0.5 ; rMin = -1.5; iMax = 1.0; iMin = -1.0; // Mapeo de la pantalla al fractal Double rRange = (rMax-rmin)/w; double iRange = (iMax-iMin)/h; int count = 0; double zr = px * rRange + rMin ; double zi = (h-py) * iRange + iMin; Ejemplos: Si px=512 dx = [0.5- (-1.5)] / 512 = 0.00390625 zr = 512 * 0.00390625 + (-1.5) = 0.5 Si px=0 dx = [0.5- (-1.5)] / 512 = 0.00390625 zr = 0 * 0.00390625 + (-1.5) = -1.5 Si px=256 dx = [0.5- (-1.5)] / 512 = 0.00390625 zr = 256 * 0.00390625 + (-1.5) = -0.5

  7. Operaciones de números complejos • class ComplexNumber {double r,i;… • Square: • r = r2– i2 • i = 2 * r * i • Add: • r = z1.r + z2.r • i = z1.i + z2.i • Mul: • r = z1.r * z2.r - z1.i * z2.i • i = z1.i * z2.r + z1.r * z2.i • Scale: • r = z1.r * scale • i = z1.i + scale • Module: • result = sqrt(r2 + i2)

  8. Manowar • c = z1(0) = z(0) • zn+1 = zn2 + z1n + c; • z1n+1 = zn;

  9. Spider • c = z(0) • zn+1 = zn2 + cn; • cn+1 = (cn/2) + zn+1 ;

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