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I was able to figure out the lines in the flame, but I am still curious about the actual process that all this goes through.
I'm still rather new to this all, however after doing my best to really read over the newer flame paper I think I might get it. From what I can see, the coefficients mentioned in the document are the x and y coordinates for the points on the triangles displayed in Apophysis (with the three x coords being a, b, and c, and the three y coords being d, e, and f). The points, represented (x,y), are plugged in and generate the points (X,Y), with X = ax + by + c, and Y = dx + ey + f, where a,b,c,d,e,f are all constants specific to the transformation. Your overall function V is taking in X and Y, and your even overall-er function F is the sum of all of your V functions, after they are multiplied to their individual values. From what I can tell (and I'm hoping someone can confirm or deny all of this), if you have a transform with, say, Linear=1 and Sinusoidal=2, then your F(X,Y) = (1 * (X,Y)) + (2 * (sin(X),sin(Y)) )
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