Flame
Flame Fractals
Flame applet.
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Description: Flame fractals are extension of IFS fractals. First they were used by Bill Poirier in 1996 at Brown University. In generalized IFS algorithm the nonlinear transformation Vi of affine function is used:
Fi(x, y) = Vj(aix + biy + ci, dix + eiy + fi)
Where:
x and y are coordinates of point,
a, b, c, d, e and f are affine coefficients,
Vj is nonlinear transformation.
Following transformations are used:
Linear: V1(x,y) = (x,y)
Sinusoidal: V2(x,y) = (sinx,siny)
Spherical: V3(x,y) = (x/r2,y/r2)
Swirl: V4(x,y) = (rcos(t+r),rsin(t+r))
HorseShoe: V6(x,y) = (rcos(2t),rsin(2t))
Polar: V7(x,y) = (t/3.14,r-1)
Handkerchief: V8(x,y) = (rsin(t+r),rcos(t-r))
Disc: V9(x,y) = (tsin(3.14r)/3.14,tcos(3.14r)/3.14)
Spiral: V10(x,y) = ((cos(t)+sin(r))/r,(sin(t)-cos(r))/r)
Hyperbolic: V11(x,y) = (sin(t)/r,cos(t)r)
Diamond: V12(x,y) = (sin(t)cos(r),cos(t)sin(r))
Ex: V13(x,y) = (rsin3(t+r),rcos(t-r))
Julia: V14(x,y) = (r0.5sin(r/2+R),r0.5cos(t/2+R))
where: R is a random wariable either 0 or 3.14,
r=(x2+y2)0.5
t=atan(y/x)
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