pikachu curve

https://gyazo.com/dbcc16aab624410ed09bcccb4e360621

code:formula

plotted for t from 0 to 52π

θ(x) is the Heaviside step function

sgn(x) is the sign of x

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) θ(51 π - t) θ(t - 47 π) + (-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) θ(47 π - t) θ(t - 43 π) + (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) θ(43 π - t) θ(t - 39 π) + (-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) θ(39 π - t) θ(t - 35 π) + (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) θ(35 π - t) θ(t - 31 π) + (-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) θ(31 π - t) θ(t - 27 π) + (-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) θ(27 π - t) θ(t - 23 π) + (-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) - 41/5 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) θ(23 π - t) θ(t - 19 π) + (-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) θ(19 π - t) θ(t - 15 π) + (-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) θ(15 π - t) θ(t - 11 π) + (236/7 sin(t + 6/5) + 1/2 sin(2 t + 47/12) - 627/5) θ(11 π - t) θ(t - 7 π) + (69/2 sin(t + 5/6) - 715/2) θ(7 π - t) θ(t - 3 π) + (-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 + 41/9) + 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) θ(3 π - t) θ(t + π)) θ(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) θ(51 π - t) θ(t - 47 π) + (-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) θ(47 π - t) θ(t - 43 π) + (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) θ(43 π - t) θ(t - 39 π) + (-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) θ(39 π - t) θ(t - 35 π) + (-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) θ(35 π - t) θ(t - 31 π) + (-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 + 41/40) + 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) θ(31 π - t) θ(t - 27 π) + (-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) θ(27 π - t) θ(t - 23 π) + (-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) θ(23 π - t) θ(t - 19 π) + (-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) θ(19 π - t) θ(t - 15 π) + (-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) θ(15 π - t) θ(t - 11 π) + (-172/5 sin(3/8 - t) + 5/4 sin(2 t + 7/2) + 2303/24) θ(11 π - t) θ(t - 7 π) + (441/5 - 455/12 sin(7/9 - t)) θ(7 π - t) θ(t - 3 π) + (-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) θ(3 π - t) θ(t + π)) θ(sqrt(sgn(sin(t/2))))