A visualization of circle-compactified 5-D Kaluza-Klein extra dimensions.

extradimenions_5D_KK_example

from vpython import *
import math

# Create a display
scene2 = canvas(title='Kaluza-Klein Extra Dimensions - 5D',
                x=0, y=0, width=1024, height=768,
                center=vector(0,-20,0), background=vector(0,0,0))



# Draw a series of parallel lines in the xy plane

gridlines=[]

L=100
H=0.1
W=0.1

for y0 in range(-25,26):
    x0=0
    z0=0

    gridlines.append(box(pos=vector(x0,y0,z0), length=L, height=H, width=W))

for x0 in range(-25,26):
    y0=0
    z0=0

    gridlines.append(box(pos=vector(x0,y0,z0), axis=vector(0,1,0), length=L, height=H, width=W))


# Now draw the curled up extra dimension at each grid point

extradimensions=[]

for y0 in range(-25,26):
    for x0 in range(-25,26):
        z0=0.40
        T=0.05
        R=abs(z0-T)
        extradimensions.append(ring(pos=vector(x0,y0,z0), axis=vector(0,1,0), radius=R,thickness=T))

This code generates this image. In the current incarnation of this code, the visualization appears in a browser window. One can then zoom and rotate to get a nice view. Here is an example of one, screen-captured and cropped.