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fractals & statistical growth 347u0 1(x , y )v(x, y)1 1(x , y )t10(x , y )3p 2 2p 3100(x , y )s00p1Figure 13.11 Left: The numbers s, t, u, and v are represented by perpendiculars to the fourvertices, with lengths proportional to their values. Right: The function 3p 2 − 2p 3 is used as amap of the noise at a point like (x,y) to others close by.The actual mapping proceeds via a number of steps (Figure 13.12):1. Transform the point (x, y) to (s x ,s y ),s x =3x 2 − 2x 3 , s y =3y 2 − 2y 3 . (13.29)2. Assign the lengths s, t, u, and v to the vertices in the mapped square.3. Obtain the height a (Figure 13.12) via linear interpolation between s and t.uv1 1(x , y )tubvt0 1(x , y )noisec(x, y)10(x , y )cx y( s,s )00(x ,y )sFigure 13.12 Left: The point (x, y) is mapped to point (s x, x y). Right: Using (13.29). Thenthree linear interpolations are performed to find c, the noise at (x, y).sa−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 347