Here is the visualization I promised. The problem with visualizing a
continous 4 dimensional vector space (i.e. the hypercube) is that between any 2 points you have an infinite number of points. But with the
discrete vector spaces you only have a finite number of points. It can be viewed as a photography series over time, so you only need to have a limited list of photographs.
I limit the number of discrete points in each dimension of the 6 dimensional cube to 2. The first 3 dimensions will then span a 2x2x2 "mini-cube". So I only need to repeat the mini-cube twice for the 4th dimension. The 5th will result in an area of 2x2 mini-cubes and the 6th dimension will result in a 2x2x2 super-cube of mini-cubes:
onbekende wrote:hypercubus is just 4
to do 6 dimensions, you need not only higher math, you need a server just for the calculations of the correct graphical represintation
As you can see, you can both visualize and understand the 6-dimensional vector space.
Movement
For moving/attacks we could allow movement along any of the dimensions (axises of the 6 dimensional coordinate system). So within the mini-cube, we allow a move either along the t, u or v dimension/axis, but not diagonally. Or the movement could go to the same point in another mini-cube that is located one step away along the x, y or z dimension/axis.
Bonuses
A bonus can be given for holding a full 3 dimensional or 4 dimensional vector space "cut" within the 6 dimensional vector space.
Lets express the full 6 dimensional vector space as t+u+v+x+y+z. A 1 dimensional cut/selection, e.g. along the t axis, could be expressed as t. A 2 dimensional cut/selection along t and u axises is expressed as t+u.
A 3 dimensional cut selection along t, u and v axises is expressed as t+u+v and can be visualized as:
A 3 dimensional cut selection along x, y and z axises is expressed as x+y+z and can be visualized as:
A 4 dimensional cut selection along t, u, y and z axises is expressed as t+u+y+z and can be visualized as:
