Biomorph

Este Fractal Biomorph, pertenece a la familia de Conjuntos de Julia donde la constante compleja C es 0.2 y el exponente de Z es 1.5.

Z_n+1 = Z_n^1.5 + 0.2

donde Z es un número complejo

Generación del Fractal Biomorph

Es muy similar al del Conjunto de Julia, la difucultad esta en evaluar Z^1.5 ya que se tratan de números complejos.

xmin = 0.06, ymin = 0.36, xmax = 0.42, ymax = 0.63, Iteraciones = 256

Observación

Como Z=ReZ + ImZi, entonces tenemos
Z=Z1.5 + 0.2
para evaluar esta expreción utilizo la rutina FloatPower que toma como
argumentos a ReZ, ImZ y me devuelve en xtmp, ytmp elevado a 1.5.
ReZ = xtmp + ReC
ImZ = ytmp + ImC
donde ReC=0.2 y ImC=0.

Código Fuente

En biomorph.zip (6 Kb) se encuentra el código completo en VisualBasic para generar la imagen de arriba, sin executable.

Sub Convercion(x As Double, y As Double, r As Double, theta As Double) If x = 0# Then If y = 0# Then r = 0# theta = 0# Else If y > 0# Then r = y theta = 0.5 * PI Else r = -y theta = -0.5 * PI End If End If Else r = Sqr(x * x + y * y) theta = Atn(y / x) If x < 0# Then If y >= 0# Then theta = PI + theta Else theta = -PI + theta End If End If End If End Sub Function Power(x As Double, y As Double) As Double If x = 0# Then If y = 0# Then Power = 1# Else Power = 0# End If Else Power = Exp(Log(x) * y) End If End Function Sub FloatPower(x As Double, y As Double, a As Double, b As Double, N As Double) Dim r As Double Dim theta As Double Dim atmp, btmp As Double If (x * x + y * y) = 0# Then If N = 0# Then a = 1# b = 0# Else a = 0# b = 0# End If Else Convercion x, y, r, theta atmp = Power(r, N) btmp = theta * N End If a = atmp * Cos(btmp) b = atmp * Sin(btmp) End Sub Private Sub AdjustAspect() Dim want_aspect As Single Dim canvas_aspect As Single Dim hgt As Single Dim wid As Single Dim mid As Single want_aspect = (ymax - ymin) / (xmax - xmin) canvas_aspect = screeny / screenx If want_aspect > canvas_aspect Then wid = (ymax - ymin) / canvas_aspect mid = (xmin + xmax) / 2 VisibleXmin = mid - wid / 2 VisibleXmax = mid + wid / 2 VisibleYmin = ymin VisibleYmax = ymax Else hgt = (xmax - xmin) * canvas_aspect mid = (ymin + ymax) / 2 VisibleYmin = mid - hgt / 2 VisibleYmax = mid + hgt / 2 VisibleXmin = xmin VisibleXmax = xmax End If End Sub Private Sub Command1_Click() Dim i, j As Integer Dim ReZ As Double Dim ImZ As Double Dim ReC, ImC As Double Dim N As Integer Dim xtmp As Double Dim ytmp As Double Dim Red As Double Dim Green As Double Dim Blue As Double AdjustAspect ReC = -0.2 ImC = 0# For j = 0 To screeny For i = 0 To screenx ReZ = ((VisibleXmax - VisibleXmin) / screenx) * i + VisibleXmin ImZ = ((VisibleYmax - VisibleYmin) / screeny) * j + VisibleYmin N = 0 Do While (N < iterationMax) And (ReZ * ReZ + ImZ * ImZ < 4) FloatPower ReZ, ImZ, xtmp, ytmp, 1.5 ReZ = xtmp + ReC ImZ = ytmp + ImC N = N + 1 Loop Red = RGBColor(N, 0) Green = RGBColor(N, 1) Blue = RGBColor(N, 2) Picture1.PSet (i, screeny - j), RGB(Red, Green, Blue) Next i Next j End Sub