Mockup of an OpenGL Gammatron shader. Post this into http://editor.thebookofshaders.com/ to get a quick visual impression.

gammatron.frag

#ifdef GL_ES
precision mediump float;
#endif

uniform vec2 u_resolution;
uniform float u_time; // this should be replaced by frame number in use
const float tau = 2.0*3.141592654;
const float direction = 1.0; // must be -1 or 1
const float tempPeriod = 0.7;
const float spacePeriod = 0.1;
const vec4 color1 = vec4(1,1,1,1);
const vec4 color2 = vec4(0,0,0,1);
const bool squareWave = false;

void main() {
    vec2 st = gl_FragCoord.xy/u_resolution.xy;
    
    float dist = distance(st, vec2(0.5));
    float phase = tau*u_time/tempPeriod*direction;
    float mixValue = (sin(tau/spacePeriod * dist + phase) + 1.0)/2.0;
    
    if(squareWave){
    mixValue = step(0.5, mixValue);}
    
    gl_FragColor = mix(color1, color2, mixValue);
}