Fourier Divergence
This is a very flexible tool for designing smooth not-repeating patterns. It uses so-called 2-dimensional Fourier function defined by a matrix. In mathematics a Fourier function is a good approximation of any analog function.
The precision of such approximation is reflected by size of its matrix. The larger matrix is, the more detailed pattern is created. In Newart maximum dimensions of a matrix are 100 x 100. It makes possible creating patterns with minimal detail size 1/100 of the canvas diagonal. But one hardly ever need such a high detail level, in most cases 10 x 10 is more than enough. The rather that large matrices have a serious impact to performance. Now let's get back to Fourier syntax.
| Fourier [overflow] | |||||||||||||
| |||||||||||||
Remarks
Definition of a Fourier function starts with parameters of so-called affine transform.
It rotates the pattern around arbitrary "focus" point and shifts it by extent of horizontal and
vertical offset. There's common practice to use random numbers in place of affine parameters.
It varies a painting but doesn't change its style.
Scale parameter is split up on horizontal and vertical parts. It defines
extent of a period. In other words scale is simply size of the pattern tile. When it's larger than canvas
the pattern doesn't repeat.
Saturation defines extent of the function peak. If it exceeds the limit an
overflow happens (when it's enabled). Overflowing visually looks like a number of curved edges with sharp
boundaries. It's managed by overflow tag. If it's not present the function never exceeds the
upper limit and the pattern looks smooth. The next pictures show a few simple designs that were
created using 3 x 3 matrices.
 |
| 0 0 0 0 0 0 0 0 1 |
 |
| 0 0 0 0 1 0 0 0 1 |
 |
| 0 0 1 0 1 0 1 0 0 |
 |
| 0 0 0 0 1 1 0 1 0 |
 |
| 0 1 0 1 1 0 0 0 0 |
 |
| 1 0 1 0 1 0 1 0 1 |
 |
| 0 1 1 0 1 0 1 1 0 |
 |
| 0 1 0 1 0 1 0 1 0 |
 |
| 0 0 1 1 0 1 1 0 0 |
Example
# Creates a stochastic fourier pattern
Fourier overflow
angle 45`
focus 0 0
offset 0 0
scale 10 10
saturation 0.25
matrix 3 x 3
random[-1:1] random[-1:1] random[-1:1]
random[-1:1] random[-1:1] random[-1:1]
random[-1:1] random[-1:1] random[-1:1]
...read about pyramid divergence