Patterns

I think I got the matrix formula for this pattern from “Introduction to Dynamics” by Percival and Richards (its certainly the pattern I remember from the book cover)

You can get different patterns if you move the slider. Python gtk code…

import pygtk
pygtk.require('2.0')
import gtk, math

class Pattern(object):
    x, y = 0, 0
    points=[]
    alpha = 76.11
    def __init__(self, xsize, ysize):
        self.xsize, self.ysize = xsize, ysize
        window = gtk.Window(gtk.WINDOW_TOPLEVEL)
        window.set_title("Pattern")
        window.connect("destroy", lambda w: gtk.main_quit())
        vbox = gtk.VBox(homogeneous=False, spacing=5)
        window.add(vbox)
        self.area = gtk.DrawingArea()
        self.area.set_size_request(xsize, ysize)
        self.area.connect("expose-event", self.area_expose_cb)
        self.area.connect("size-allocate", self.calculate_points)

        slider = gtk.Adjustment(value=self.alpha, lower=0.0,
                                upper=100.0, step_incr=0.01)
        slider.connect("value-changed", self.slider_changed)
        self.hscale = gtk.HScale(slider)
        vbox.pack_start(self.area, expand=True, fill=True, padding=0)
        vbox.pack_start(self.hscale, expand=False)
        window.show_all()

    def slider_changed(self, slider):
        self.alpha = slider.get_value()
        self.calculate_points()

    def calculate_points(self, area=None, event=None):
        x, y, self.xsize, self.ysize = self.area.get_allocation()
        xscale = self.xsize/2.0
        yscale = self.ysize/2.0
        m = 52
        angle = self.alpha*math.pi/180.0
        c = math.cos(angle)
        s = math.sin(angle)
        self.points=[]
        try:
            for j in range(m):
                x = 0
                y = j/float(m)
                for n in range(200):
                    w = x
                    x = x*c - (y - x*x)*s
                    y = w*s + (y - w*w)*c
                    if abs(x)>4 or abs(y)>4: raise StopIteration()
                    if x>1 or y>1: continue
                    self.points.append((int(x*xscale+xscale), int(y*yscale+yscale)))
        except StopIteration:
            self.area.queue_draw()

    def area_expose_cb(self, area, event):
        blue = self.area.get_colormap().alloc_color("#0000FF")
        pointgc = self.area.window.new_gc()
        pointgc.set_foreground(blue)
        area.window.draw_point(pointgc, 20, 10)
        self.area.window.draw_points(pointgc, self.points)

def main():
    gtk.main()
    return 0

if __name__ == '__main__':
    Pattern(600, 500)
    main()