Mock up wave equation example

Light strip outputs aren't hooked up yet

interactions.py

@@ -1,4 +1,4 @@
-from math import pi, cos, sin
+from math import pi, cos, sin, exp
 
 import pygame, colorsys
 
@@ -11,7 +11,7 @@ vertices = [(viewsize*(1 + shrink*x)/2, viewsize*(1 + shrink*y)/2) for x, y in
   [(0, 0)] + [(cos(-n*pi/5), sin(-n*pi/5)) for n in range(10)] + [(0, 0)]
 ]
 
-# edges as vertex pairs
+# edges as vertex pairs. FireStar will rest on vertices 6 (A), 5 (B), 7 (C)
 edges = [
   (0, 1), (0, 3), (0, 5), (0, 7), (0, 9),
   (2, 8), (2, 6), (6, 10), (10, 4), (4, 8),
@@ -41,36 +41,90 @@ cyc_edge_adj = [
   (14, 11), (11, 23), (23, 20), (20, 17), (17, 14)
 ]
 
+# === interaction parameters ===
+
+frame_rate = 24
+inductance = 0.001
+drain = False
+drain_rate = 0.1
+
 # === phase space ===
 
-litness = 30*[0]
+charge = 12*[0]
+current = 30*[0]
 
 # === main loop ===
 
 if __name__ == '__main__':
   # set up display and clock
-  pygame.display.init()
+  pygame.init()
-  screen = pygame.display.set_mode((viewsize, viewsize))
+  screen = pygame.display.set_mode((viewsize, viewsize + 100))
   pygame.display.set_caption('Preview')
+  font = pygame.font.Font(None, 25)
   clock = pygame.time.Clock()
   
+  # set up background
+  background = pygame.Surface(screen.get_size()).convert()
+  background.fill((32, 32, 32))
+  
   to_light = 0
   while True:
+    # handle events
     for event in pygame.event.get():
-      if event.type == pygame.QUIT:
+      if event.type == pygame.KEYDOWN:
+        if event.key == pygame.K_j:
+          charge[0] += 10
+          charge[11] -= 10
+        elif event.key == pygame.K_k:
+          charge[0] += 100
+          charge[11] -= 100
+        elif event.key == pygame.K_SPACE:
+          drain = True
+        pygame.draw.aaline(screen, (255, 255, 255), (0, 0), (viewsize, viewsize))
+      elif event.type == pygame.KEYUP:
+        if event.key == pygame.K_SPACE:
+          drain = False
+      elif event.type == pygame.QUIT:
         quit()
     
-    litness[to_light] = 1.
+    # print data
+    energy = 0.5*(sum(q*q for q in charge) + inductance*sum(i*i for i in current))
+    screen.blit(background, (0, 0))
+    text = font.render('energy', True, (255, 255, 255))
+    screen.blit(text, (20, viewsize))
+    text = font.render(str(energy), True, (255, 255, 255))
+    screen.blit(text, (120, viewsize))
+    text = font.render('charge[0]', True, (255, 255, 255))
+    screen.blit(text, (20, 30 + viewsize))
+    text = font.render(str(charge[0]), True, (255, 255, 255))
+    screen.blit(text, (120, 30 + viewsize))
+    
+    # show state
     for e in range(30):
+      litness = 1 - exp(-2*current[e]*current[e])
+      color = colorsys.hsv_to_rgb(0.45 + litness*0.25, 1 - 0.5*litness*litness, litness)
+      ##color = colorsys.hsv_to_rgb(litness*0.167, 1 - 0.5*litness*litness, litness)
       pygame.draw.aaline(
         screen,
-        tuple(255*c for c in colorsys.hsv_to_rgb(e/30., litness[e], 0.2 + 0.8*litness[e])),
+        tuple(255*c for c in color),
         vertices[edges[e][0]],
         vertices[edges[e][1]],
       )
-      litness[e] *= 0.9
+    
+    # evolve state. use verlet integration, first updating the currents and then
+    # using the new currents to update the charges.
+    for e in range(30):
+      u, v = edges[e]
+      ##current[e] *= 1 - resistance
+      current[e] += inductance*(charge[u] - charge[v])
+    for e in range(30):
+      u, v = edges[e]
+      charge[u] -= current[e]
+      charge[v] += current[e]
+    if drain:
+      for v in range(12):
+        charge[v] *= 1 - drain_rate
     
     # step
-    to_light = (to_light + 1) % 30
     pygame.display.flip()
-    clock.tick(24)
+    clock.tick(frame_rate)