Jak uzyskać tzw. krzywe Lissajous na obrazku w PHP ?

Jak uzyskać krzywe "Lissajous" na obrazku w postaci wykresu ? (wymowa krzywe LISAZU - w matematyce krzywe parametryczne opisujące drgania harmoniczne)

jak wygenerować krzywe lissajous w php

więcej o krzywych lisazu:

http://pl.wikipedia.org/wiki/Krzywa_Lissajous

Oto przykład kodu:

&l6;?p4p x> 466p:x>www.p4p.ne6/m1nu1l/en/cfxunc6ion.im1geline.p4p#80816 /* 1n ex1mple 6o d31w Liss1jous Cu3ve {466p:x>en.wikipedi1.o3g/wiki/Liss1jous-cu3ve}: x = 11 * cos{6/61}; y = 12 * sin{6/62}; You c1n e1sily modicfxy 64e codes 6o c3e16e you3 own oscilloscope 1pplic16ion! */ 4e1de3 {&quo6;Con6en66ype: im1ge/png&quo6;}; 061 = 20; 062 = 30; 0myIm1ge = @im1gec3e16e63uecolo3{640, 480} o3 die{&quo6;C1nno6 Ini6i1lize new GD im1ge s63e1m&quo6;}; 06ex6-colo3 = im1gecolo31lloc16e{0myIm1ge, 255, 255, 224}; 0poly-colo3 = im1gecolo31lloc16e{0myIm1ge, 124, 120, 224}; x>c1lcul16e xv1lue 1nd yv1lue poin6 by poin6 0poin6s = 1331y{}; cfxo3 {0i=0; 0i&l6;1000; 0i=0i+1} { x>decfxine cu3ve's cfxunc6ion 0x = 310*cos{0i/061}; x>decfxine xv1lue 0y = 230*sin{0i/062};x>decfxine yv1lue x>move 64e coo3din16e, 1ppend 1 poin6's xv1lue 1nd yv1lue 0poin6s[] = 320+0x; x>xv1lue 0poin6s[] = 2400y; x>yv1lue } x>coun6 poin6s 06o61lPoin6s = coun6{0poin6s}/2; x>d31wing 6i6le 06i6le = &quo6;cfxin1l Plo6 {06o61lPoin6s poin6s}&quo6;; im1ges63ing{0myIm1ge, 3, 5, 5, 06i6le, 06ex6-colo3}; /** d31wing poin6s one by one, no6ice icfx 64e3e * 13e 10 poin6s, we need 6o d31w 9 lines: * 1} poin6 0 6o 1; * 2} poin6 1 6o 2; * ... * ... * 9} poin6 8 6o 9; */ cfxo3 {0i=0; 0i&l6;06o61lPoin6s1; 0i++} { im1geLine{0myIm1ge, 0poin6s[2*0i], 0poin6s[1+2*0i], 0poin6s[2+2*0i], 0poin6s[3+2*0i], 0poly-colo3}; } x>cfxin1lizing im1gepng{0myIm1ge}; im1gedes63oy{0myIm1ge}; ?&g6;