Datei:Lorentz Transform Animation.gif
Größe dieser Vorschau: 256 × 256 Pixel.
Originaldatei (256 × 256 Pixel, Dateigröße: 232 KB, MIME-Typ: image/gif, Endlosschleife, 128 Bilder, 7,7 s)
Beschreibung
| Beschreibung |
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. |
| Datum | |
| Quelle | Eigenes Werk |
| Urheber | Drummyfish |
| GIF‑Erstellung | |
| 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 = (
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l \n"
" l "
)
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
|
Lizenz
Ich, der Urheber dieses Werkes, veröffentliche es unter der folgenden Lizenz:
 
|
Diese Datei wird unter der Creative-Commons-Lizenz CC0 1.0 Verzicht auf das Copyright zur Verfügung gestellt. |
| Die Person, die das Werk mit diesem Dokument verbunden hat, übergibt dieses weltweit der Gemeinfreiheit, indem sie alle Urheberrechte und damit verbundenen weiteren Rechte – im Rahmen der jeweils geltenden gesetzlichen Bestimmungen – aufgibt. Das Werk kann – selbst für kommerzielle Zwecke – kopiert, modifiziert und weiterverteilt werden, ohne hierfür um Erlaubnis bitten zu müssen.
|
Dateiversionen
Klicke auf einen Zeitpunkt, um diese Version zu laden.
| Version vom | Vorschaubild | Maße | Benutzer | Kommentar | |
|---|---|---|---|---|---|
| aktuell | 21:34, 1. Apr. 2019 | | 256 × 256 (232 KB) | wikimediacommons>Drummyfish | General improvement |
Dateiverwendung
Die folgende Seite verwendet diese Datei:
