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 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.