MathArt: 4th Dimension Illustrations
The following project is a collaboration with Mathematician Shanna Dobson, on the conceptual representation of the 4th physical dimension.
If the 4th variable in such a dimension is spatial, what would the system look like? The following illustrations aims to aid the paper in visualizing many of its concepts.
The full paper: Categorical Mental Imagery: Visualizing the 4th Spatial Dimension
can be accessed Here
Shanna Dobson
https://www.calstatela.edu/faculty/shanna-dobson
MathArt Visualization
Illustration 1.
The 4th Variable "w" in a 4-dimension system, shown here moving towards one direction, resulting in the folding/unfolding of inside/outside surface of the same object
Illustration 2.
A 4th dimension ∞-perspective tunnel when viewing from a 1-point single origin perspective. The orange represents the "inside" and blue the "outside".
Illustration 3.
Simultaneous Expansion/Shrinking of two "sides" of the same surface with w coordinate change
Illustration 4.
Spatial perspective origin observing the 4th dimension coordinate systems
Illustration 5.
Concept of a dual-axis 4th spatial dimension, one axis represent the "inside" and another the "outside" surface
Illustration 6.
Topology concept of the "sideless" definition in 4th spatial dimension
Animation 1.
Left. The shrinking "Inside" perspective
Right.The expanding 'Outside" perspective
Animation 2.
Combined perspectives of "Inside" and "Outside", this serves as a exploration of how might a 4th dimension perspective works