Strange Attractors

attractors.py

# coding: utf-8

# attractors.py
# 10 March 2016
#
# Copyright 2016 Jason Milldrum
#
# Draw various attractors in a GTK window
# See:
# https://en.wikipedia.org/wiki/Lorenz_system
# https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor
# https://en.wikipedia.org/wiki/Chua%27s_circuit

import math
import gi
import cairo
gi.require_version('Gtk', '3.0')
from gi.repository import Gtk

class MyWindow(Gtk.Window):
    def __init__(self):
        Gtk.Window.__init__(self, title="Strange Attractors")
        self.move(100, 100)

        self.vbox = Gtk.Box(orientation=Gtk.Orientation.VERTICAL, spacing=6)
        self.add(self.vbox)

        self.stack = Gtk.Stack()
        self.stack.set_transition_type(Gtk.StackTransitionType.SLIDE_LEFT_RIGHT)
        self.stack.set_transition_duration(300)

        self.lorenz_drawing = Gtk.DrawingArea()
        self.lorenz_drawing.set_size_request(400, 400)
        self.lorenz_drawing.connect("draw", self.draw_lorenz)
        self.stack.add_titled(self.lorenz_drawing, "lorenz", "Lorenz Attractor")
        #self.vbox.pack_start(self.drawing, True, True, 0)
        #self.add(self.drawing)

        self.rossler_drawing = Gtk.DrawingArea()
        self.rossler_drawing.set_size_request(400, 400)
        self.rossler_drawing.connect("draw", self.draw_rossler)
        self.stack.add_titled(self.rossler_drawing, "rossler", "Rössler Attractor")

        self.chua_drawing = Gtk.DrawingArea()
        self.chua_drawing.set_size_request(400, 400)
        self.chua_drawing.connect("draw", self.draw_chua)
        self.stack.add_titled(self.chua_drawing, "chua", "Chua's Circuit")

        self.stack_switcher = Gtk.StackSwitcher()
        self.stack_switcher.set_stack(self.stack)

        self.switcher_align = Gtk.Alignment(xalign=0.5, yalign=0.0, xscale=0.0, yscale=0.0)
        self.switcher_align.add(self.stack_switcher)

        self.vbox.pack_start(self.stack, True, True, 0)
        self.vbox.pack_start(self.switcher_align, False, False, 0)

        self.lorenz_coords = []
        self.rossler_coords = []
        self.chua_coords = []

    def draw_lorenz(self, widget, cr):
        center_x = self.get_size()[0] / 2
        center_y = self.get_size()[1] / 2
        scale_x = self.get_size()[0] / 70.0
        scale_y = self.get_size()[1] / 70.0
        offset_y = center_y * 0.9

        cr.set_line_width(1)
        cr.set_source_rgb(0.0, 0.0, 0.0)
        cr.move_to(center_x, center_y - offset_y)

        for i in self.lorenz_coords:
            # Draw the X-Z view
            cr.line_to((i[0] * scale_x) + center_x, (i[2] * scale_y) + center_y - offset_y)

        cr.stroke()

        # Draw axes legend
        cr.set_source_rgb(0.6, 0.0, 0.0)
        cr.select_font_face("Courier", cairo.FONT_SLANT_NORMAL,
        cairo.FONT_WEIGHT_BOLD)
        cr.set_font_size(24)

        (x, y, width, height, dx, dy) = cr.text_extents("X")

        cr.move_to(center_x - width / 2, self.get_size()[1] - 40)
        cr.show_text("X")

        (x, y, width, height, dx, dy) = cr.text_extents("Z")

        cr.move_to(self.get_size()[0] - width - 10, center_y)
        cr.show_text("Z")

    def draw_rossler(self, widget, cr):
        center_x = self.get_size()[0] / 2
        center_y = self.get_size()[1] / 2
        scale_x = self.get_size()[0] / 60.0
        scale_y = self.get_size()[1] / 60.0
        offset_y = center_y * 0.01

        cr.set_line_width(1)
        cr.set_source_rgb(0.0, 0.0, 0.0)
        cr.move_to(center_x, center_y - offset_y)

        for i in self.rossler_coords:
            # Draw the X-Y view
            cr.line_to((i[0] * scale_x) + center_x, (i[1] * scale_y) + center_y - offset_y)

        cr.stroke()

        # Draw axes legend
        cr.set_source_rgb(0.6, 0.0, 0.0)
        cr.select_font_face("Courier", cairo.FONT_SLANT_NORMAL,
        cairo.FONT_WEIGHT_BOLD)
        cr.set_font_size(24)

        (x, y, width, height, dx, dy) = cr.text_extents("X")

        cr.move_to(center_x - width / 2, self.get_size()[1] - 40)
        cr.show_text("X")

        (x, y, width, height, dx, dy) = cr.text_extents("Y")

        cr.move_to(self.get_size()[0] - width - 10, center_y)
        cr.show_text("Y")

    def draw_chua(self, widget, cr):
        center_x = self.get_size()[0] / 2
        center_y = self.get_size()[1] / 2
        scale_x = self.get_size()[0] / 10.0
        scale_y = self.get_size()[1] / 10.0
        offset_y = center_y * 0.01

        cr.set_line_width(1)
        cr.set_source_rgb(0.0, 0.0, 0.0)
        cr.move_to(center_x, center_y - offset_y)

        for i in self.chua_coords:
            # Draw the X-Z view
            cr.line_to((i[0] * scale_x) + center_x, (i[2] * scale_y) + center_y - offset_y)

        cr.stroke()

        # Draw axes legend
        cr.set_source_rgb(0.6, 0.0, 0.0)
        cr.select_font_face("Courier", cairo.FONT_SLANT_NORMAL,
        cairo.FONT_WEIGHT_BOLD)
        cr.set_font_size(24)

        (x, y, width, height, dx, dy) = cr.text_extents("X")

        cr.move_to(center_x - width / 2, self.get_size()[1] - 40)
        cr.show_text("X")

        (x, y, width, height, dx, dy) = cr.text_extents("Z")

        cr.move_to(self.get_size()[0] - width - 10, center_y)
        cr.show_text("Z")

    def lorenz(self):
        h = 0.01
        sigma = 10.0
        rho = 28.0
        beta = 8.0 / 3.0
        x0 = 0.1
        y0 = 0.0
        z0 = 0.0

        for i in range(10000):
            x1 = x0 + h * sigma * (y0 - x0)
            y1 = y0 + h * (x0 * (rho - z0) - y0)
            z1 = z0 + h * (x0 * y0 - beta * z0)
            x0 = x1
            y0 = y1
            z0 = z1
            self.lorenz_coords.append([x0, y0, z0])

    def rossler(self):
        h = 0.02
        a = 0.1
        b = 0.1
        c = 14.0
        x0 = 0.1
        y0 = 0.0
        z0 = 0.0

        for i in range(15000):
            x1 = x0 + h * (-y0 - z0)
            y1 = y0 + h * (x0 + a * y0)
            z1 = z0 + h * (b + z0 * (x0 - c))
            x0 = x1
            y0 = y1
            z0 = z1
            self.rossler_coords.append([x0, y0, z0])

    def chua(self):
        h = 0.005
        alpha = 15.6
        beta = 28.0
        d = -5.0 / 7.0
        e = -8.0 / 7.0
        x0 = 0.7
        y0 = 0.0
        z0 = 0.0
        f = lambda x: d * x + 0.5 * (e - d) * (abs(x + 1) - abs(x - 1))

        for i in range(15000):
            x1 = x0 + h * (alpha * (y0 - x0 - f(x0)))
            y1 = y0 + h * (x0 - y0 + z0)
            z1 = z0 + h * (-beta * y0)
            x0 = x1
            y0 = y1
            z0 = z1
            self.chua_coords.append([x0, y0, z0])

win = MyWindow()
win.connect("delete-event", Gtk.main_quit)
win.show_all()
win.lorenz()
win.rossler()
win.chua()
Gtk.main()