The Meaning Behind Fractional Dimensions
The mathematics behind realistic computer-generated images.
We all know how dimensions work. The first dimension is a straight line. To locate a position on a straight line, we need only one number. Hence, 1 dimension. A plane requires two numbers. That’s 2 dimensions. We need three numbers to locate a position in space. Space has 3 dimensions.
What could we possibly describe as having, say, 2 ½ dimensions?
Suppose we have a linear measure of 1 unit. We can double it, and now it has length 2.
Take a unit square. Double each linear measure. Each side, which had length 1, now has length 2. What has happened to the area?
The length increases by a factor of 2×2=4. Enlarge the edges of a cube by a factor of two, and its volume increases by a factor of 2×2×2=8.
Enlargement in 1 dimension corresponds to creating 2¹ copies of the original. Enlargement in 2 dimensions, 2² copies and 3…
