It's pretty simple and I have specially given the code in python which demonstrates the concept. For details on Attractors please refer wikipedia. I have used the Python pygame module for graphics.
Here's the end result:-
![[Image: GOVr9W9.png]](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_un1Fr49lFTOxZ2pR1IA9aY65N7uVYlmSf2aXUapotYD3V3uDOFvb7qKkDoPqamXa-_oqI8Wi_g1r8hh9sTkd29Ew=s0-d)
Here's the code:
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| ''' | |
| Created on 17-Jan-2015 | |
| @author: Psycho_Coder | |
| ''' | |
| from math import sin, cos | |
| from PIL import Image | |
| import pygame, sys, os | |
| from pygame.locals import QUIT, KEYDOWN, K_ESCAPE | |
| class Attractor(): | |
| ''' | |
| Class for Attractor functions and methods | |
| ''' | |
| def __init__( self, constants = {"a":-0.89, "b": 1.59, "c":1.85, "d": 2.19} ): | |
| ''' | |
| Constructor | |
| ''' | |
| # Useful Constants | |
| os.environ['SDL_VIDEO_CENTERED'] = '1' # Center Screen the Window | |
| pygame.init() | |
| self.size = self.width, self.height = ( 1024, 640 ) | |
| self.screen = pygame.display.set_mode( self.size, 0, 32 ) | |
| pygame.display.set_caption( "Peter D. Jong Attractor" ) | |
| # Colors | |
| self.bg = ( 248, 248, 248 ) | |
| self.textshade = ( 48, 48, 48 ) | |
| self.grayshade = ( 144, 144, 144 ) | |
| self.constants = constants | |
| self.no_of_ite = 50000; | |
| self.xn, self.yn = 1, 1 | |
| self.coords = [] | |
| self.screen.fill( self.bg ) | |
| self.count = 0 | |
| self.str_values = "a =" + str( self.constants["a"] ) + ", b = " + str( self.constants["b"] ) + ", c = " \ | |
| + str( self.constants["c"] ) + ", d = " + str( self.constants["d"] ) | |
| # Different Font Objects | |
| self.font_obj = pygame.font.Font( "lunchds.ttf", 22 ) | |
| self.font_obj2 = pygame.font.Font( "retganon.ttf", 24 ) | |
| self.text_surf_obj1 = self.font_obj.render( "Peter D. Jong Attractor", True, self.textshade, None ) | |
| self.text_rect_obj1 = self.text_surf_obj1.get_rect() | |
| self.text_rect_obj1.center = 200, 40 | |
| self.text_surf_obj2 = self.font_obj2.render( self.str_values , True, self.textshade, None ) | |
| self.text_rect_obj2 = self.text_surf_obj2.get_rect() | |
| self.text_rect_obj2.center = self.width // 2 + 60, self.height - 25 | |
| self.screen.blit( self.text_surf_obj1, self.text_rect_obj1 ) | |
| self.screen.blit( self.text_surf_obj2, self.text_rect_obj2 ) | |
| self.game_loop() | |
| def game_loop( self ): | |
| while True: | |
| for evt in pygame.event.get(): | |
| if evt.type == QUIT or ( evt.type == KEYDOWN and evt.key == K_ESCAPE ): | |
| pygame.quit() | |
| sys.exit() | |
| if self.count > self.no_of_ite: | |
| self.save_surface( "pdf1.png" ) | |
| sys.exit() | |
| else: | |
| for i in range( 10000 ): | |
| self.xn, self.yn = ( sin( self.constants["a"] * self.yn ) - cos ( self.constants["b"] \ | |
| * self.xn ) ), ( sin( self.constants["c"] * self.xn ) - cos( self.constants["d"] * self.yn ) ) | |
| # xn, yn = ( d * sin( a * xn ) - sin ( b * yn ) ), ( c * cos( a * xn ) + cos( b * yn ) ) | |
| self.coords.append( ( self.xn, self.yn ) ) | |
| pygame.draw.circle( self.screen, self.grayshade , ( self.width // 2 + \ | |
| int( 120 * self.xn ), self.height // 2 + int( 120 * self.yn ) ), 1, 1 ) | |
| self.count += 1 | |
| pygame.display.update() | |
| def save_surface( self, filename ): | |
| if filename != None: | |
| data = pygame.image.tostring( self.screen, 'RGBA' ) | |
| img = Image.fromstring( 'RGBA', self.size, data ) | |
| pygame.image.save( self.screen, filename ) | |
| else: | |
| raise ValueError( "The filename is not given." ) | |
| if __name__ == "__main__": | |
| ins = Attractor() |
I have used two custom fonts as you can see in the code above. You can get them from here and here. You can use either system font or download two new fonts and put them in the same execution directory. Make sure you edit the code with proper font names.
self.xn, self.yn = ( sin( self.constants["a"] * self.yn ) - cos ( self.constants["b"] \ * self.xn ) ), ( sin( self.constants["c"] * self.xn ) - cos( self.constants["d"] * self.yn ) ) # xn, yn = ( d * sin( a * xn ) - sin ( b * yn ) ), ( c * cos( a * xn ) + cos( b * yn ) ) self.coords.append( ( self.xn, self.yn ) ) pygame.draw.circle( self.screen, self.grayshade , ( self.width // 2 + \ int( 120 * self.xn ), self.height // 2 + int( 120 * self.yn ) ), 1, 1 )
Changing the constants a,b, c and varying the number of iteration you can create many more custom shapes. So be creative and start hacking!
