# Mandelbrot evolution

20 mai 2008

As promised in my previous post, here is a more evolved version of my Python simple Mandelbrot generator. This version adds color and zoom support, but it remains limited — it is meant to be simple, plus I’m still a Python beginner.

Read more to get the commented source :)

``````[python]import mathfrom Tkinter import *# Global variablescwidth = 300        # Width of the canvascheight = 300        # Height of the canvasloops = 200         # Maximum number of iterationszoomf = 4           # Zoom factorcomputing = False   # Wether we're being computing the fractal or not# Global mandelbrot window coordinatesmx1 = -2my1 = 2mx2 = 2my2 = -2# Create a simple (and ugly) color palettedef make_palette(loops):        # Create an empty array    palette = []        for i in range (0, loops):                # Generate an hex color code biased toward red        c = ((i * 1000) + 0xDD9900) % 0xFFFFFF                # Format the color code as #FFFFFF        color = "#%06X" % c        palette.append(color)            # The end of the palette must be black...    palette[loops-1] = "#000"    # ... and the start too    palette[0] = "#000"    palette[1] = "#000"        # Return the palette array    return palette# Mandelbrot function# cv : canvas# palette : the color palette array# x1, y1 : coordinates of the uper left point of the window# x2, y2 : coordinates of the bottom right point of the windowdef mandel(cv, palette, x1, y1, x2, y2):    # Clear the canvas    cv.delete(ALL)    # Compute the x and y increment    dx = float(abs(x2 - x1)) / cwidth    dy = float(abs(y2 - y1)) / cheight        # Let's start the maths    y = y1    for j in range(0, cheight):        x = x1        for i in range(0, cwidth):                        x = x + dx            c = complex(x, y)            a = 0            # Core loop : x = x^2 + c, loop n times, see if the number escape a circle centered on 0            for k in range(0, loops):                a = a*a + c                if abs(a) > 4:                    break                        # Draw a plot of a color from the palette,            # depending of when the point escaped from the loop            cv.create_line(i, j, i, j + 1, fill = palette[k])                    y = y - dy        cv.update()# Compute a rectangular zoom window from the zoom factor# cx, cy : coordinates of the center of the zoom window# unZoom : specifies if we're unzooming instead of the default zoomingdef computeZoomRect(cx, cy, unZoom = False):    global mx1, mx2, my1, my2, zoomf    if unZoom:        width = abs(mx2 - mx1) * float(zoomf)        height = abs(my2 - my1) * float(zoomf)    else:        width = abs(mx2 - mx1) / float(zoomf)        height = abs(my2 - my1) / float(zoomf)    mousex = (cx / float(cwidth)) * abs(mx2 - mx1) + mx1    mousey =  -(cy / float(cheight)) * abs(my2 - my1) + my1            zoomRect = [0, 0, 0, 0]    zoomRect[0] = mousex - (width / float(2))    zoomRect[1] = mousey + (height / float(2))    zoomRect[2] = mousex + (width / float(2))    zoomRect[3] = mousey - (height / float(2))    return zoomRect# Draw a preview of the zoom window on the canvasdef mouseMove(event):    global c, cwidth, cheight, zoomf, zoomRect, computing        # Draw rectangle only if we finished to compute the fractal    if computing == True:        return        # Compute rect half-width and half-height    hwidth = (cwidth / zoomf) / 2    hheight = (cheight / zoomf) / 2    # Delete previous zoom Rect    c.delete(zoomRect)        # Create a new zoomRect around the current mouse location    zoomRect = c.create_rectangle(event.x - hwidth, event.y - hheight, event.x + hwidth, event.y + hheight, width=1)        return# Zoom functiondef zoom(event):    global mx1, mx2, my1, my2, c, palette, computing        # If we are already computing, do nothing and return    if computing == True:        return        # Compute a zoom window    rect = computeZoomRect(event.x, event.y)        # Update the global coordinates    mx1 = rect[0]    my1 = rect[1]    mx2 = rect[2]    my2 = rect[3]        # Draw the fractal    computing = True    mandel(c, palette, mx1, my1, mx2, my2)    computing = False        return    # Unzoom functiondef unzoom(event):    global mx1, mx2, my1, my2, c, palette        # If we are already computing, do nothing and return    if computing == True:        return        # Compute a zoom window    rect = computeZoomRect(event.x, event.y, True)        # Update the global coordinates    mx1 = rect[0]    my1 = rect[1]    mx2 = rect[2]    my2 = rect[3]        # Draw the fractal    computing = True    mandel(c, palette, mx1, my1, mx2, my2)    computing = False        return# Create window and canvasroot = Tk()c = Canvas(root,width = cwidth, height = cheight)zoomRect = c.create_rectangle(0,0,0,0)c.pack()# Register eventsc.bind('', zoom)c.bind('', unzoom)c.bind('', mouseMove)# Create the palettepalette = make_palette(loops)# Draw first mandelbrotcomputing = Truemandel(c, palette, mx1, my1, mx2, my2)computing = False# Run event looproot.mainloop()
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