Pikachu en séries de Fourier !

C'est admirable, isn't it Lulu ? ;)

La formule:

x(t) = ((-1/4 sin(10/7-23 t)-3/10 sin(4/3-22 t)-2/5 sin(7/5-19 t)-1/5 sin(7/5-16 t)-3/7 sin(10/7-15 t)-3/8 sin(13/9-9 t)-19/13 sin(11/7-3 t)+222/5 sin(t+11/7)+41/2 sin(2 t+11/7)+34/9 sin(4 t+11/7)+1/3 sin(5 t+8/5)+3/8 sin(6 t+8/5)+12/7 sin(7 t+13/8)+11/7 sin(8 t+13/8)+1/4 sin(10 t+20/13)+2/9 sin(11 t+16/9)+3/8 sin(12 t+8/5)+1/3 sin(13 t+7/4)+1/2 sin(14 t+17/10)+5/7 sin(17 t+17/10)+1/28 sin(18 t+9/2)+1/2 sin(20 t+12/7)+3/7 sin(21 t+16/9)+6/11 sin(24 t+7/4)-979/9) theta(51 pi-t) theta(t-47 pi)+(-6/5 sin(14/9-22 t)-1/9 sin(7/5-19 t)-9/8 sin(14/9-18 t)-1/14 sin(15/11-15 t)-6/5 sin(11/7-12 t)-7/6 sin(11/7-8 t)-29/10 sin(11/7-6 t)-104/3 sin(11/7-2 t)+415/18 sin(t+11/7)+71/18 sin(3 t+11/7)+19/8 sin(4 t+33/7)+22/21 sin(5 t+8/5)+3/8 sin(7 t+61/13)+5/9 sin(9 t+11/7)+1/8 sin(10 t+14/3)+4/7 sin(11 t+11/7)+4/11 sin(13 t+14/3)+1/7 sin(14 t+14/3)+2/7 sin(16 t+5/3)+1/6 sin(17 t+5/3)+6/7 sin(20 t+8/5)+1/7 sin(21 t+5/3)+1/6 sin(23 t+8/5)-2765/8) theta(47 pi-t) theta(t-43 pi)+(1189/22 sin(t+11/7)+3/4 sin(2 t+13/8)+11/2 sin(3 t+8/5)+2/7 sin(4 t+17/7)+22/9 sin(5 t+18/11)+1/4 sin(6 t+17/7)+16/17 sin(7 t+20/11)+1/5 sin(8 t+29/9)-1627/7) theta(43 pi-t) theta(t-39 pi)+(-3/7 sin(1/18-5 t)-3/4 sin(1/2-3 t)+109/9 sin(t+13/10)+5/8 sin(2 t+11/3)+5/9 sin(4 t+10/3)+3/10 sin(6 t+21/8)+2/9 sin(7 t+2/3)+1/4 sin(8 t+23/8)-1190/9) theta(39 pi-t) theta(t-35 pi)+(188/21 sin(t+27/28)+2/5 sin(2 t+17/6)+2/3 sin(3 t+91/23)+3/8 sin(4 t+53/18)+2/11 sin(5 t+1/7)-369) theta(35 pi-t) theta(t-31 pi)+(-8/9 sin(1/10-12 t)-34/9 sin(10/9-6 t)-137/10 sin(5/7-2 t)+26/5 sin(t+13/4)+118/5 sin(3 t+11/8)+43/8 sin(4 t+13/7)+49/6 sin(5 t+11/12)+22/5 sin(7 t+13/4)+17/16 sin(8 t+1/7)+5/4 sin(9 t+1/4)+5/7 sin(10 t+17/5)+29/15 sin(11 t+5/6)-1915/8) theta(31 pi-t) theta(t-27 pi)+(-2/7 sin(10/7-7 t)-sin(1/27-4 t)+68/7 sin(t+44/15)+76/9 sin(2 t+37/10)+30/7 sin(3 t+1)+8/9 sin(5 t+3/2)+4/5 sin(6 t+31/8)+3/7 sin(8 t+10/3)+6/13 sin(9 t+8/7)+1/3 sin(10 t+31/9)-2135/9) theta(27 pi-t) theta(t-23 pi)+(-3/8 sin(1/4-23 t)-3/5 sin(1/8-22 t)-13/8 sin(5/4-20 t)-9/7 sin(3/2-16 t)-42/5 sin(4/3-4 t)+768/7 sin(t+11/5)+109/5 sin(2 t+16/7)+150/13 sin(3 t+11/6)+33/7 sin(5 t+97/24)+23/4 sin(6 t+5/7)+69/7 sin(7 t+9/8)+32/5 sin(8 t+21/5)+7/6 sin(9 t+22/9)+28/5 sin(10 t+5/6)+43/10 sin(11 t+26/7)+14/9 sin(12 t+5/11)+13/9 sin(13 t+40/9)+11/6 sin(14 t+2/5)+3/2 sin(15 t+17/10)+7/11 sin(17 t+4/3)+3/8 sin(18 t+31/10)+4/7 sin(19 t+14/9)+6/5 sin(21 t+17/7)+4/7 sin(24 t+27/8)+1006/11) theta(23 pi-t) theta(t-19 pi)+(-63/8 sin(2/7-8 t)-38/13 sin(11/9-6 t)-14/5 sin(1/17-4 t)+77/9 sin(t+1/2)+52/7 sin(2 t+10/3)+22/9 sin(3 t+76/17)+21/8 sin(5 t+26/7)+3 sin(7 t+15/8)+64/7 sin(9 t+57/14)+6 sin(10 t+17/6)-544/7) theta(19 pi-t) theta(t-15 pi)+(-37/10 sin(4/7-5 t)-3 sin(3/7-3 t)+24/7 sin(t+7/6)+9/7 sin(2 t+2/5)+31/15 sin(4 t+37/8)+9/5 sin(6 t+12/5)+59/12 sin(7 t+13/6)+15/7 sin(8 t+25/8)+134/15 sin(9 t+7/3)+73/8 sin(10 t+1/5)-4406/11) theta(15 pi-t) theta(t-11 pi)+(236/7 sin(t+6/5)+1/2 sin(2 t+47/12)-627/5) theta(11 pi-t) theta(t-7 pi)+(69/2 sin(t+5/6)-715/2) theta(7 pi-t) theta(t-3 pi)+(-19/9 sin(6/5-21 t)-37/10 sin(7/9-19 t)-23/8 sin(1-17 t)-16/3 sin(7/6-16 t)-29/5 sin(1/5-9 t)-919/11 sin(1/7-3 t)+1573/6 sin(t+91/45)+214/5 sin(2 t+33/8)+421/14 sin(4 t+13/8)+61/6 sin(5 t+19/5)+401/16 sin(6 t+43/14)+511/51 sin(7 t+35/8)+144/7 sin(8 t+5/6)+137/10 sin(10 t+25/13)+18/7 sin(11 t+15/7)+17/9 sin(12 t+42/9)+9/7 sin(13 t+13/7)+29/10 sin(14 t+22/7)+25/8 sin(15 t+1/4)+12/5 sin(18 t+11/8)+14/5 sin(20 t+27/7)+13/8 sin(22 t+12/7)+7/6 sin(23 t+7/9)+26/11 sin(24 t+23/7)-1891/8) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))

y(t) = ((-8/11 sin(11/8-22 t)-1/2 sin(10/7-21 t)+67/6 sin(t+33/7)+1478/29 sin(2 t+11/7)+3/5 sin(3 t+30/7)+26/3 sin(4 t+11/7)+1/6 sin(5 t+13/9)+30/29 sin(6 t+8/5)+2/5 sin(7 t+14/3)+88/29 sin(8 t+8/5)+1/4 sin(9 t+31/7)+11/8 sin(10 t+8/5)+1/16 sin(11 t+9/2)+1/12 sin(12 t+5/4)+1/10 sin(13 t+25/11)+11/8 sin(14 t+18/11)+2/7 sin(15 t+37/8)+1/6 sin(16 t+11/8)+2/9 sin(17 t+5/3)+1/5 sin(18 t+17/10)+1/13 sin(19 t+19/8)+23/24 sin(20 t+12/7)+7/11 sin(23 t+9/5)+9/7 sin(24 t+7/4)-1538/7) theta(51 pi-t) theta(t-47 pi)+(-2/7 sin(20/13-23 t)-1/6 sin(3/2-20 t)-5/7 sin(20/13-17 t)-1/9 sin(20/13-11 t)-1/6 sin(13/9-9 t)-19/6 sin(17/11-3 t)+263/5 sin(t+11/7)+614/15 sin(2 t+11/7)+87/10 sin(4 t+11/7)+1/7 sin(5 t+11/8)+19/11 sin(6 t+11/7)+7/5 sin(7 t+11/7)+4/3 sin(8 t+8/5)+9/5 sin(10 t+14/9)+4/7 sin(12 t+8/5)+3/11 sin(13 t+3/2)+1/8 sin(14 t+22/15)+1/9 sin(15 t+12/7)+6/5 sin(16 t+11/7)+2/9 sin(18 t+11/7)+3/5 sin(19 t+8/5)+1/26 sin(21 t+15/11)+6/7 sin(22 t+8/5)-1867/8) theta(47 pi-t) theta(t-43 pi)+(118/39 sin(t+11/7)+40/7 sin(2 t+33/7)+49/25 sin(3 t+14/3)+12/5 sin(4 t+8/5)+1/9 sin(5 t+32/13)+5/2 sin(6 t+13/8)+2/5 sin(7 t+22/5)+3/4 sin(8 t+7/4)-143/10) theta(43 pi-t) theta(t-39 pi)+(-1/8 sin(2/3-8 t)-1/2 sin(7/5-2 t)-246/19 sin(1/7-t)+1/4 sin(3 t+33/16)+1/6 sin(4 t+17/6)+1/5 sin(5 t+31/7)+1/11 sin(6 t+50/17)+1/8 sin(7 t+30/7)+665/6) theta(39 pi-t) theta(t-35 pi)+(-119/10 sin(7/15-t)+2/11 sin(2 t+25/7)+2/9 sin(3 t+5/8)+1/5 sin(4 t+33/7)+1/4 sin(5 t+19/10)+1023/10) theta(35 pi-t) theta(t-31 pi)+(-1/7 sin(2/7-12 t)-1/8 sin(3/10-5 t)+25/7 sin(t+77/17)+355/59 sin(2 t+42/40)+27/5 sin(3 t+46/15)+33/7 sin(4 t+11/3)+27/10 sin(6 t+13/9)+5/11 sin(7 t+11/5)+5/8 sin(8 t+3)+8/5 sin(9 t+16/15)+16/15 sin(10 t+1/7)+7/9 sin(11 t+12/5)-862/7) theta(31 pi-t) theta(t-27 pi)+(-1/3 sin(5/4-8 t)-2/5 sin(5/9-7 t)-5/7 sin(11/8-5 t)-7/2 sin(15/14-2 t)+29/8 sin(t+41/10)+11/6 sin(3 t+13/3)+7/6 sin(4 t+1/27)+2/7 sin(6 t+8/7)+1/9 sin(9 t+9/5)+2/7 sin(10 t+1/10)+201/5) theta(27 pi-t) theta(t-23 pi)+(-4/11 sin(8/9-12 t)-10/7 sin(19/13-10 t)+623/3 sin(t+10/7)+39/5 sin(2 t+10/11)+251/9 sin(3 t+4/3)+5/7 sin(4 t+4/3)+61/6 sin(5 t+4/3)+14/9 sin(6 t+23/7)+76/25 sin(7 t+9/7)+3/4 sin(8 t+1/4)+19/5 sin(9 t+3/2)+17/6 sin(11 t+6/5)+13/8 sin(13 t+14/13)+8/9 sin(14 t+17/6)+24/25 sin(15 t+1/2)+1/6 sin(16 t+13/8)+5/8 sin(17 t+1)+1/7 sin(18 t+18/17)+6/7 sin(19 t+1)+1/4 sin(20 t+4/9)+2/7 sin(21 t+7/5)+1/3 sin(22 t+8/7)+2/5 sin(23 t+1/26)+2/11 sin(24 t+8/7)-243/8) theta(23 pi-t) theta(t-19 pi)+(-111/10 sin(4/5-9 t)-12/5 sin(7/13-2 t)+1/6 sin(t+48/11)+13/8 sin(3 t+27/7)+71/24 sin(4 t+6/11)+22/9 sin(5 t+7/2)+19/7 sin(6 t+8/17)+20/7 sin(7 t+34/9)+55/7 sin(8 t+6/5)+64/9 sin(10 t+38/9)+27/5) theta(19 pi-t) theta(t-15 pi)+(-22/7 sin(4/3-8 t)-19/7 sin(20/13-6 t)+38/13 sin(t+1/24)+12/11 sin(2 t+5/9)+26/7 sin(3 t+7/9)+11/5 sin(4 t+12/11)+37/10 sin(5 t+17/10)+51/10 sin(7 t+10/3)+33/4 sin(9 t+26/7)+41/5 sin(10 t+9/5)-27/2) theta(15 pi-t) theta(t-11 pi)+(-172/5 sin(3/8-t)+5/4 sin(2 t+7/2)+2303/24) theta(11 pi-t) theta(t-7 pi)+(441/5-455/12 sin(7/9-t)) theta(7 pi-t) theta(t-3 pi)+(-1/3 sin(1/20-18 t)-7/5 sin(7/9-17 t)-18/11 sin(2/5-14 t)-24/5 sin(1/13-9 t)+2767/7 sin(t+11/3)+229/5 sin(2 t+17/7)+313/8 sin(3 t+22/5)+32/3 sin(4 t+22/5)+169/6 sin(5 t+21/8)+23/7 sin(6 t+26/11)+21/2 sin(7 t+5/6)+55/6 sin(8 t+14/5)+212/13 sin(10 t+24/7)+26/9 sin(11 t+9/2)+16/5 sin(12 t+25/6)+35/17 sin(13 t+4/11)+15/8 sin(15 t+7/10)+2/3 sin(16 t+20/9)+16/7 sin(19 t+4/5)+13/7 sin(20 t+29/7)+14/3 sin(21 t+7/5)+4/3 sin(22 t+7/4)+12/7 sin(23 t+34/33)+7/4 sin(24 t+27/7)-211/5) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t/2))))

Et si on la trace avec t entre 0 et 52π

Source:

Pikachu, attaque séries de Fourier !


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Allez voir sur Wolfram Alpha Pikachu curve, et ils parlent aussi de la "courbe des Rolling Stones" ou celle de "Dark Vador".

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