The Settings menu can change the color of each set of lines in the N-cubes, the background color
and the "dots" or corners of the N-cube. Line thickness (width) can also be changed.
The next picture is of a 4-space, twisted-circle N-cube. It's called a circle-cube because the
points of the cube are evenly spaced around the edges of a circle. It is "twisted" due to the
connectivity of the points which were placed in sequential order around the circle. The colors of
the line sets, background and dots have been changed from their default values by picking (clicking)
a color square and then dropping (clicking) it onto one of the numbered lineset rectangles in the
"Set Lineset Colors" section of the Settings Menu.
The next picture is the same 4-space cube plotted as an untwisted circle-cube. It is called "untwisted" because the sequential order of the points has been altered to create an N-cube that appears to have had its lines "uncrossed" or "straightened out".
A newer (incomplete) version of the program enables the user to search for specially defined, maximal length closed loops called N-space snakes. A maximal length 5-space snake is shown below.
Ncube.exe will plot up to 7-space cubes. At that point there are so many lines between so many points
that displaying them becomes almost pointless, although it helps if the cube is drawn with thinner lines.
In the following picture the "levels" of points become obvious. There is one point on the top level,
seven on the second, 21 on the third, and 35, 35, 21, 7 and 1 on the remaining levels in order. The
number of points on each level of every N-space cube corresponds to the values in Pascal's triangle -
resulting in the name "Pascal's N-cube".
Pascal's Triangle 0 1 1 1 1 2 1 2 1 3 1 3 3 1 4 1 4 6 4 1 5 1 5 10 10 5 1 6 1 6 15 20 15 6 1 7 1 7 21 35 35 21 7 1
