harmonograph is usually seen in the Science Museum in machinery and equipment, it has two or more of the pendulum with a pen, you can draw on a piece of paper. Put pen movements pen on paper to draw beautiful patterns. By plotting orthogonal sinusoidal act together on the drawing point can be easily simulated in the computer program it. This generates Lissajous (Lissajous-Figure), these graphics will be attenuated to form a pleasing "parallel" nested line, just as you see in the bill.
It is fast, and can be faster (or slower) provided as needed. Tip: The display window to full screen. MIT License; from GitHub Download
#!/usr/bin/python
''' Spectral Harmonographs Copyright 2014 Alan Richmond (Tuxar.uk)
'''
print("Quit: q key, Screenshot: spacebar")
import pygame, sys, random as r
from pygame.locals import *
from math import pi, sin, cos, exp
# EDIT THESE:
width,height=1280,720 # YouTube HD
width,height=1920,1080 # my left monitor
width,height=1280,1024 # my right monitor
width,height=1680,1050 # Lucy's monitor
width,height=1200,800
#width,height=2560,1440 # YT channel art
dd=0.99995 # decay factor
dt=0.02 # time increment
speed=200 # yes, speed
hui=57*2 # Hue increment
hue,sat,val,aaa=0,100,100,0
sd=0.005 # frequency spread (from integer)
mx=4 # max range for amplitudes & frequencies
print("Hit SPACE to save")
def check_event():
global save
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:
save=True
print("Saving when finished...")
def scale(length):
while True:
a1,a2=r.randint(-mx,mx),r.randint(-mx,mx)
max=abs(a1)+abs(a2)
if max>0: break
return a1,a2,length/(2*max)
steps=0
pygame.init()
pygame.event.set_allowed([QUIT, KEYDOWN])
screen = pygame.display.set_mode((width,height),DOUBLEBUF)
screen.set_alpha(None)
#fg=pygame.Color(0,0,0,0)
#fg=(0,0,0)
fg=(255,255,255)
save=False
while True:
# Amplitudes & scales
ax1,ax2,xscale=scale(width)
ay1,ay2,yscale=scale(height)
fx1, fx2 = r.randint(1,mx) + r.gauss(0,sd), r.randint(1,mx) + r.gauss(0,sd)
fy1, fy2 = r.randint(1,mx) + r.gauss(0,sd), r.randint(1,mx) + r.gauss(0,sd)
px1, px2 = r.uniform(0,2*pi), r.uniform(0,2*pi)
py1, py2 = r.uniform(0,2*pi), r.uniform(0,2*pi)
print(ax1,ax2,ay1,ay2)
print(fx1,fx2,fy1,fy2)
print(px1,px2,py1,py2)
dec=1.0
t=0.0 # angle for sin
first=True
while dec>0.015:
# calculate next x,y point along line
x = xscale * dec * (ax1*sin(t * fx1 + px1) + ax2*sin(t * fx2 + px2)) + width/2
y = yscale * dec * (ay1*sin(t * fy1 + py1) + ay2*sin(t * fy2 + py2)) + height/2
dec*=dd # decay
if not first: # ignore any complaint about prev_x,y being undefined
# fg.hsva=(hue,sat,val,aaa)
# hue = (hue + dt*hui) % 360 # cycle hue
pygame.draw.aaline(screen, fg, (x, y), (prev_x, prev_y), 1)
else:
first=False
prev_x = x # save x,y for next line segment start
prev_y = y
if steps%speed==0: pygame.display.update()
steps+=1
t+=dt # increment angle for sin
check_event()
if save: # parameters are encoded into filename
pars='shg-{0}_{1}-{2}_{3}-{4}_{5}'.format(ax1,ax2,fx1,fx2,px1,px2)
pygame.image.save(screen, pars+'.jpg')
print("Saved as "+pars+'.jpg')
save=False
screen.fill((0,0,0))
# screen.fill((255,255,255))
sudo apt-get install pygame
sudo apt-get install python
Save it into your directory, it executable and run it:
chmod +x harmonograph.py
./harmonograph.py
Renderings:
