## Generating random image animation sequences

**Introduction**

A random animation sequence is sometimes useful as a controlled, noisy background
for visual stimulus studies. The following programs use Fourier synthesis of
image sequences from filtered, random, complex frequency distrubutions. A 3D
complex array (x,y,time) is shaped according to the desired filter function,
inverse-Fourier transformed, and displayed as an image sequence. Fourier synthesis
guarantees periodicity in time (for seamless looping). The programs we used
were either band-limited to a certain spatial and temporal frequency range,
or fractal in space and bandlimited in time. Example animations are given below.
Programs were written in Matlab 6.5.

** The programs**

The first program produces a bandlimited
(in space and time) animation. You can select the bandwidth in terms of cycles/image-width
and cycles/total-animation-length. This example
used spatial frequencies between 4 and 10, and temporal frequencies below 3.
The second example uses spatial frequencies
between 1 and 5, and temporal frequencies below 3. The third
example uses spatial frequencies between 1 and 5, and temporal frequencies
below 6. Higher spatial frequencies mean more fine detail. Higher temporal frequencies
mean faster motion. A bigger example with
spatial frequencies between 4 and 10, and temporal frequencies below 3.

The second program produces an approximate
fractal (in space) animation. This is done by filtering the spatial frequency
amplitudes by a power-law of frequency. The first
example used a -2.5 spatial power law, and a time bandwidth of 3. As the
power law strength is reduced toward -1, the image becomes "rougher".
The second example has a power law of -1.5,
but the same time bandwidth. The third example
has a power law of -2.0.
A bigger example with fractal dimension -2 and bandlimited to 4 cycles.