You may have seen those devices at the Science Museum or Exploratorium or Techniquest… There’s a drawing surface and some arrangement of pendula with a pen touching the paper on the drawing surface, set in motion it draws these pretty pictures, which are essentially decaying Lissajous figures. Lissajous figures are often seen in old sci-fi movies, on an oscilloscope, where you apply sine waves of different frequencies in the x,y axes. I read about these as a young boy and created my own by suspending a torch (flashlight) from the ceiling by 3 threads in a darkened room, with a camera set to time exposure on the floor, pointing up at the swinging torch. And when I got access to computers with graphics capabilities I programmed the mathematical simulation. If you search the web for ‘encyclogram’ you’ll find my ancient Java version.So anyway, here’s my Python Harmonograph (much improved one now on GitHub; also one in 3D!)
''' Harmonograph. Trace of 6 decaying sine waves, 3 per axis (x & y)(i.e. 3-pendula) Quit with q key, screenshot with s key Uses PyGame for IO. ''' import pygame import sys import time import tempfile from math import pi, sin, cos from pygame.locals import * pygame.init() p2=1.57 p4=p2/2.0 # Edit these: ax = [-2,2,0] ay = [1.5,1.5,0] fx = [-1,.99,.5] fy = [.99,1,.49] px = [0,p2,0] py = [p4,0,0] dd=0.00003 black=(0,0,0) # Fore- and background colors white=(255,255,255) bg=black fg=white inc=0.04 width,height=1024,768 # Window size aspect=width/height*1.0 yscale=120 xscale=yscale*aspect d=1 # resolution screen = pygame.display.set_mode((width,height)) # You can add FULLSCREEN as last parameter screen.fill(bg) t=0.0 # angle for sin first=True while 1: for event in pygame.event.get(): if event.type == QUIT: sys.exit() elif event.type == KEYDOWN and event.key == K_q: sys.exit() elif event.type == KEYDOWN and event.key == K_SPACE: restart=True elif event.type == KEYDOWN and event.key == K_s: pars="a,f,p(x,y)="+str(ax)+str(ay)+str(fx)+str(fy)+str(px)+str(py) myfont = pygame.font.SysFont("monospace", 15) label = myfont.render(pars, 1, (100,100,100)) screen.blit(label, (100, height-15)) tf=tempfile.NamedTemporaryFile(prefix='hg', suffix='.jpg', dir ='.', delete=False) pygame.image.save(screen, tf.name) # calculate next x,y point along line x = xscale * d * (ax[0]*sin(t * fx[0] + px[0]) + ax[1]*sin(t * fx[1] + px[1]) + ax[2]*sin(t * fx[2] + px[2])) + width/2 y = yscale * d * (ay[0]*cos(t * fy[0] + py[0]) + ay[1]*cos(t * fy[1] + py[1]) + ay[2]*cos(t * fy[2] + py[2])) + height/2 d = d - dd if not first: # ignore any complaint about prev_x,y being undefined pygame.draw.aaline(screen, fg, (x, y), (prev_x, prev_y), 2) else: first=False prev_x = x # save x,y for next line segment start prev_y = y pygame.display.update() t+=inc # increment angle for sin