math - Generating movement based on time t for real time ocean waves from an initial spectrum -

I've spent the past week or so using a simple ocean using the Jörstner waves, but the tile roof There are problems with it, so I have decided

Using IFFT, a height field immerses my toes in suspicious water of presentation.

frequency spectrum

2) Use it to convert vertical domain to spatial domain by using ifft to create height fields - of time Animating with

From the beginning of this journey I have learned about things Complex Plane, Complex Exponent Equation, FFT and more detail etc. But after the initial steps to make the initial spectrum (still providing a texture made of the Gusli number with the average 0 filtered 0 and the SD with Philips spectrum) is still completely lost.

My code is here to create initial data (GLSL):

  Float Phillips spectrum (vec2k) {// kLen is the Line = line of float = length ( Kashmir) depth of vector from center; Float kSq = kLen * kLen; // amp wave dimension; passed as a similar float amp = dimension; // l = velocity * valico / gravity float l = (velocity * velocity) / 9.81; Float dior = dot (normally (wavelength), normal (k)); Return Emp * (Dior * Die) * XP (-1.0 / (KSAC * L * L)) / (KSQ * s); } Zero main () {vec3 amount; // Screenshows are found - From center 0.0 and 0.0 / 0.5 in both directions // vec2 screenpos = VC2 (gl_FragCoord.x, gl_FragCoord.y) / Texys - vec2 (0.5,0.5); // random GUAS number vec2 random gag = vec2 (rand (screenpos), rand (screen grid.Yx)); // Freipal spectrum is used as a filter depending on location in the fractal domain float Phil = sqrt (Philips spectrum); Boat coeff = 1.0 / sqrt (2.0); Color = VC3 (coeff * randomGuass.x * Phil, Cauff * Random Gaussian * Phil, 0.0); }  

which makes texture like this:

Now how have I completely lost: a) Get the spectrum in three directions from the initial texture

b) According to the slides, animate it according to the time described in this paper. 5

I can be completely stupid and really ignore something - I have seen many letters and only myself Even after getting it lost in the formulas. help please.