File:Lorentz Transform Animation.gif
Summary
| Description |
English: This file recreates this file, except this one is free of copyright restrictions. I created it myself by writing an own script in Python, and I release it under CC0.
The animation shows the effect of Lorentz transform used in theory of relativity. An observer moving along a world line (red) is shown along with random events in space-time (black dots). The diagonal grey lines indicate the speed of light. Compare this to Galilean transform. |
| Date | |
| Source | Own work Category:PNG created with Python#Lorentz%20Transform%20Animation.gif |
| Author | Drummyfish |
| Source code | # space transformation animation in Python
# by Drummyfish
# released under CC0 1.0
from PIL import Image
import random
import math
TRANSFORM_TYPE = 0 # 0 = galileian, 1 = lorentz
SPEED_OF_LIGHT = 1
SIZE = 256
TRAJECTORY = (
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)
TRAJECTORY_POINTS = [(i.find("l") - 20) * 0.5 for i in TRAJECTORY.split("\n")]
TRAJECTORY_POINTS.reverse()
random.seed(35)
EVENTS = [(random.randrange(SIZE * 40) - 20 * SIZE,random.randrange(len(TRAJECTORY_POINTS))) for i in range(500)]
def draw_square(pixels, x, y, r, c):
x -= r / 2
y -= r / 2
x2 = x + r
y2 = y + r
x = max(0,x)
y = max(0,y)
x2 = min(SIZE - 1,x2)
y2 = min(SIZE - 1,y2)
for j in range(y,y2):
for i in range(x,x2):
pixels[i,j] = c
def transform_galilean(relative, velocity):
return (int(relative[0] - velocity * relative[1]),relative[1])
def transform_lorentz(relative, velocity):
sol2 = SPEED_OF_LIGHT * SPEED_OF_LIGHT
factor = 1.0 / math.sqrt(1.0 - velocity * velocity / sol2)
return (int(factor * (relative[0] - velocity * relative[1])),
int(factor * (relative[1] - (velocity * relative[0]) / sol2)))
def draw_event(relative_event, velocity, pixels, color, size):
transformed = transform_galilean(relative_event,velocity) if TRANSFORM_TYPE == 0 else transform_lorentz(relative_event,velocity)
screen = (SIZE / 2 + transformed[0],SIZE / 2 - transformed[1])
draw_square(pixels,screen[0],screen[1],size,color)
image = Image.new("RGB",(SIZE,SIZE),"white")
pixels = image.load()
v_previous = 0
for f in range(len(TRAJECTORY_POINTS)): # for each frame
for j in range(SIZE): # clear the canvas
for i in range(SIZE):
relative_y = SIZE / 2 - j
helper_line = (relative_y == 0) or (relative_y % 32 == 0 and i % 4 == 0)
if TRANSFORM_TYPE == 1:
relative_x = SIZE / 2 - i
if abs(relative_x / float(relative_y if relative_y != 0 else 0.0001)) == SPEED_OF_LIGHT:
helper_line = True
pixels[i,j] = (200,200,200) if helper_line else (255,255,255)
x = TRAJECTORY_POINTS[f]
# compute average velocity over several trajectory points, for smooth movement:
avg = 10
weight_sum = 0
v = 0
for n in range(avg):
index = f - n + avg / 2
weight = avg / 2 - abs(avg / 2 - n) + 1
v += weight * (TRAJECTORY_POINTS[(index + 1) % len(TRAJECTORY_POINTS)] - TRAJECTORY_POINTS[index % len(TRAJECTORY_POINTS)])
weight_sum += weight
v = v / float(weight_sum)
v = (v + v_previous) / 2.0 # this smooths acceleration
v_previous = v
for k in range(-2,3): # draw events
for e in EVENTS:
relative = (e[0] - x,e[1] - f + k * len(TRAJECTORY_POINTS))
draw_event(relative,v,pixels,(0,0,0),3)
for n in range(SIZE): # draw the trajectory
index = n - SIZE / 2
trajectory_index = (f + index) % len(TRAJECTORY_POINTS)
relative = (TRAJECTORY_POINTS[trajectory_index] - x, index)
draw_event(relative,v,pixels,(255,0,0),2)
draw_square(pixels,SIZE / 2,SIZE / 2,7,(0,0,255)) # draw the observer
image.save("out" + str(f).zfill(4) + ".png") # save the frame
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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Category:Animated GIF files
Category:Animations of geometry
Category:Animations of special relativity
Category:Animations of theory of relativity
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Category:Images with Python source code
Category:Lorentz boosts
Category:PNG created with Python
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Category:Self-published work