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Input interpretation:

CatDog-like curve  (popular curve) | image


Associated character:

Cat Dog


Equations:

Parametric equations:

x(t) = ((-59\/2 sin(11\/7-3 t)+267\/7 sin(t+33\/7)+99\/49 sin(2 t+13\/8)+50\/3 sin(4 t+11\/7)+59\/6 sin(5 t+11\/7)+79\/16 sin(6 t+33\/7)+69\/7 sin(7 t+33\/7)+19\/8 sin(8 t+11\/7)+29\/4 sin(9 t+11\/7)+9\/4 sin(10 t+17\/11)+22\/7 sin(11 t+11\/7)+103\/51 sin(12 t+11\/7)-2449\/6) theta(95 pi-t) theta(t-91 pi)+(-1\/5 sin(11\/7-12 t)-37\/10 sin(11\/7-10 t)-8\/5 sin(11\/7-6 t)-34\/3 sin(11\/7-4 t)-192\/5 sin(11\/7-t)+134\/7 sin(2 t+33\/7)+35\/6 sin(3 t+33\/7)+23\/5 sin(5 t+11\/7)+7\/9 sin(7 t+11\/7)+2\/3 sin(8 t+11\/7)+77\/26 sin(9 t+11\/7)+18\/17 sin(11 t+8\/5)+1834\/5) theta(91 pi-t) theta(t-87 pi)+(251\/2 sin(t+8\/5)+17\/16 sin(2 t+7\/2)+83\/6 sin(3 t+11\/7)+4\/9 sin(4 t+19\/7)+29\/6 sin(5 t+5\/3)+1\/8 sin(6 t+38\/9)+11\/4 sin(7 t+18\/11)+2\/7 sin(8 t+27\/8)+19\/13 sin(9 t+8\/5)+1\/8 sin(10 t+13\/5)+19\/20 sin(11 t+16\/9)+1\/13 sin(12 t+29\/8)-4463\/6) theta(87 pi-t) theta(t-83 pi)+(-1\/33 sin(4\/7-10 t)-25\/9 sin(11\/7-8 t)-98\/9 sin(11\/7-5 t)-59\/13 sin(11\/7-3 t)+83\/6 sin(t+11\/7)+53\/6 sin(2 t+11\/7)+29\/7 sin(4 t+11\/7)+139\/6 sin(6 t+11\/7)+9\/2 sin(7 t+14\/9)+3\/7 sin(9 t+8\/5)+sin(11 t+33\/7)+1\/31 sin(12 t+4)-2824\/3) theta(83 pi-t) theta(t-79 pi)+(-13\/8 sin(11\/7-11 t)-9\/7 sin(17\/11-10 t)-81\/5 sin(11\/7-7 t)-506\/13 sin(11\/7-6 t)-49\/4 sin(14\/9-4 t)+52\/9 sin(t+11\/7)+35\/4 sin(2 t+11\/7)+141\/20 sin(3 t+11\/7)+47\/3 sin(5 t+11\/7)+3\/7 sin(8 t+8\/7)+18\/11 sin(9 t+3\/2)+3\/8 sin(12 t+33\/7)-3897\/8) theta(79 pi-t) theta(t-75 pi)+(-28\/19 sin(11\/7-9 t)+9 sin(t+33\/7)+291\/7 sin(2 t+8\/5)+155\/12 sin(3 t+8\/5)+10\/3 sin(4 t+8\/5)+5\/2 sin(5 t+33\/7)+4\/3 sin(6 t+11\/7)+6\/7 sin(7 t+7\/4)+25\/6 sin(8 t+8\/5)+5\/11 sin(10 t+14\/9)+2\/7 sin(11 t+12\/7)+2\/5 sin(12 t+5\/3)+3373\/6) theta(75 pi-t) theta(t-71 pi)+(-17\/11 sin(15\/14-5 t)-13\/4 sin(4\/7-3 t)+(205 sin(t))\/8+6\/5 sin(2 t+2\/7)+7\/4 sin(4 t+11\/6)-3251\/7) theta(71 pi-t) theta(t-67 pi)+(-5\/6 sin(5\/7-2 t)+839\/10 sin(t+9\/2)+44\/5 sin(3 t+17\/4)+3\/4 sin(4 t+7\/4)-2279\/4) theta(67 pi-t) theta(t-63 pi)+(681\/5 sin(t+37\/8)+3\/5 sin(2 t+16\/7)+43\/3 sin(3 t+31\/7)+3\/5 sin(4 t+9\/4)+131\/26 sin(5 t+17\/4)-104\/3) theta(63 pi-t) theta(t-59 pi)+(974\/11 sin(t+7\/5)+40\/13 sin(2 t+17\/4)+64\/7 sin(3 t+1)+19\/9 sin(4 t+68\/15)+47\/16 sin(5 t+2\/3)+7\/4 sin(6 t+35\/8)+13\/10 sin(7 t+3\/8)+1355\/8) theta(59 pi-t) theta(t-55 pi)+(-263\/3 sin(1\/48-t)+46\/7 sin(2 t+1\/13)-967\/3) theta(55 pi-t) theta(t-51 pi)+(69\/10 sin(t+18\/7)+94 sin(2 t+101\/25)+23\/7 sin(3 t+127\/42)+13\/9 sin(4 t+6\/7)+14\/13 sin(5 t+40\/9)+59\/9 sin(6 t+5\/2)+3\/4 sin(7 t+8\/3)+9\/10 sin(8 t+2\/3)+8\/5 sin(9 t+26\/7)+11\/6 sin(10 t+5\/6)+1\/3 sin(11 t+27\/8)-6475\/8) theta(51 pi-t) theta(t-47 pi)+(-11\/8 sin(1\/3-10 t)+39\/8 sin(t+5\/3)+763\/10 sin(2 t+75\/19)+47\/7 sin(3 t+39\/10)+37\/8 sin(4 t+6\/11)+14\/9 sin(5 t+19\/5)+9\/2 sin(6 t+3\/8)+7\/4 sin(7 t+31\/7)+26\/27 sin(8 t+20\/21)+5\/4 sin(9 t+23\/6)+8\/5 sin(11 t+39\/11)+6\/5 sin(12 t+2\/3)+9663\/11) theta(47 pi-t) theta(t-43 pi)+(-11\/6 sin(1\/5-3 t)+13\/3 sin(t+11\/6)+43\/10 sin(2 t+23\/8)+27\/13 sin(4 t+19\/6)-7483\/9) theta(43 pi-t) theta(t-39 pi)+(-8\/5 sin(1\/5-5 t)-53\/8 sin(1\/5-3 t)-24\/7 sin(5\/9-2 t)+19\/3 sin(t+8\/3)+14\/9 sin(4 t+3)-4604\/7) theta(39 pi-t) theta(t-35 pi)+(218\/31 sin(t+11\/5)+103\/17 sin(2 t+17\/4)+9\/5 sin(3 t+43\/10)+10\/7 sin(4 t+23\/8)+38\/37 sin(5 t+1\/2)+4\/7 sin(6 t+3)+5783\/10) theta(35 pi-t) theta(t-31 pi)+(-2\/5 sin(7\/5-5 t)-3\/2 sin(5\/6-3 t)+43\/6 sin(t+5\/4)+19\/10 sin(2 t+9\/5)+1\/2 sin(4 t+37\/18)+1\/4 sin(6 t+6\/5)+2821\/4) theta(31 pi-t) theta(t-27 pi)+(-23\/8 sin(2\/7-3 t)-15\/7 sin(9\/7-2 t)+105\/2 sin(t+18\/17)+23\/12 sin(4 t+49\/11)+5\/9 sin(5 t+4)-4915\/6) theta(27 pi-t) theta(t-23 pi)+(-5\/3 sin(1-4 t)-10\/7 sin(3\/5-2 t)+129\/2 sin(t+5\/4)+16\/5 sin(3 t+2\/5)+5\/8 sin(5 t+99\/25)-15751\/25) theta(23 pi-t) theta(t-19 pi)+(119\/3 sin(t+3\/4)+710) theta(19 pi-t) theta(t-15 pi)+(-151\/50 sin(1\/23-2 t)+633\/8 sin(t+16\/15)+6451\/11) theta(15 pi-t) theta(t-11 pi)+(-1\/4 sin(4\/5-12 t)-5\/8 sin(1\/17-10 t)-9\/10 sin(2\/7-8 t)-7\/9 sin(3\/8-6 t)+109\/6 sin(t+5\/3)+6\/5 sin(2 t+1\/2)+27\/5 sin(3 t+20\/9)+13\/8 sin(4 t+4\/9)+8\/5 sin(5 t+23\/10)+2\/5 sin(7 t+7\/2)+3\/7 sin(9 t+61\/20)+1\/3 sin(11 t+23\/6)-3107\/8) theta(11 pi-t) theta(t-7 pi)+(-1\/2 sin(5\/8-11 t)-5\/8 sin(2\/3-9 t)-804\/35 sin(3\/8-t)+4 sin(2 t+10\/11)+44\/7 sin(3 t+2\/7)+5\/2 sin(4 t+1\/8)+5\/2 sin(5 t+6\/5)+7\/3 sin(6 t+2\/9)+5\/7 sin(7 t+18\/7)+12\/7 sin(8 t+17\/18)+5\/7 sin(10 t+29\/14)+1\/6 sin(12 t+12\/5)+2065\/6) theta(7 pi-t) theta(t-3 pi)+(-2\/3 sin(7\/5-36 t)-3\/4 sin(8\/7-34 t)-19\/7 sin(12\/13-24 t)-5 sin(17\/16-23 t)-14\/9 sin(7\/11-22 t)-4 sin(3\/5-18 t)-46\/7 sin(4\/5-17 t)-59\/15 sin(1\/4-14 t)-89\/6 sin(17\/11-10 t)-49\/11 sin(5\/7-8 t)-27 sin(4\/3-6 t)-1687\/10 sin(7\/10-2 t)+9392\/13 sin(t+25\/9)+219\/4 sin(3 t+14\/9)+213\/2 sin(4 t+21\/11)+107\/5 sin(5 t+1\/5)+157\/4 sin(7 t+3\/4)+242\/27 sin(9 t+14\/3)+107\/7 sin(11 t+11\/10)+67\/5 sin(12 t+5\/7)+26\/3 sin(13 t+5\/4)+50\/7 sin(15 t+18\/7)+31\/8 sin(16 t+14\/5)+23\/4 sin(19 t+7\/4)+25\/9 sin(20 t+24\/7)+86\/17 sin(21 t+29\/9)+19\/6 sin(25 t+1\/7)+2\/5 sin(26 t+2\/5)+13\/8 sin(27 t+17\/8)+5\/4 sin(28 t+22\/5)+4\/5 sin(29 t+3)+4\/7 sin(30 t+10\/11)+17\/10 sin(31 t+6\/13)+6\/5 sin(32 t+32\/7)+5\/3 sin(33 t+32\/9)+6\/7 sin(35 t+1\/6)+15\/14 sin(37 t+17\/9)+15\/14 sin(38 t+15\/8)+3\/5 sin(39 t+13\/6)-118\/17) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t\/2))))\ny(t) = ((-37\/7 sin(11\/7-3 t)-283\/9 sin(11\/7-2 t)+22 sin(t+11\/7)+179\/8 sin(4 t+11\/7)+59\/8 sin(5 t+11\/7)+77\/5 sin(6 t+11\/7)+257\/16 sin(7 t+11\/7)+17\/3 sin(8 t+11\/7)+89\/7 sin(9 t+33\/7)+13\/6 sin(10 t+8\/5)+3\/7 sin(11 t+9\/7)+6\/7 sin(12 t+14\/9)-4538\/11) theta(95 pi-t) theta(t-91 pi)+(-13\/8 sin(11\/7-12 t)-2\/5 sin(22\/15-10 t)-3\/4 sin(11\/7-7 t)-51\/2 sin(11\/7-3 t)-211\/5 sin(11\/7-t)+207\/16 sin(2 t+11\/7)+102\/5 sin(4 t+11\/7)+135\/7 sin(5 t+11\/7)+5\/9 sin(6 t+3\/2)+26\/7 sin(8 t+11\/7)+25\/6 sin(9 t+11\/7)+6\/7 sin(11 t+11\/7)-2890\/7) theta(91 pi-t) theta(t-87 pi)+(-1\/2 sin(7\/5-12 t)-2\/9 sin(7\/5-9 t)-2\/5 sin(7\/5-8 t)-1\/3 sin(16\/11-7 t)-4\/11 sin(14\/9-5 t)-1\/6 sin(10\/7-4 t)-3\/7 sin(10\/7-3 t)-12\/7 sin(11\/7-2 t)+24\/5 sin(t+8\/5)+1\/5 sin(6 t+14\/9)+1\/12 sin(10 t+11\/6)+1\/35 sin(11 t+1\/6)+659\/20) theta(87 pi-t) theta(t-83 pi)+(-1\/2 sin(11\/7-11 t)-47\/19 sin(11\/7-4 t)-11\/9 sin(11\/7-3 t)+305\/17 sin(t+33\/7)+5\/7 sin(2 t+33\/7)+43\/9 sin(5 t+11\/7)+97\/10 sin(6 t+11\/7)+53\/8 sin(7 t+11\/7)+8\/5 sin(8 t+14\/9)+5\/9 sin(9 t+14\/9)+5\/9 sin(10 t+14\/9)+1\/4 sin(12 t+14\/3)+1741\/30) theta(83 pi-t) theta(t-79 pi)+(-2\/9 sin(17\/11-10 t)-29\/7 sin(11\/7-7 t)-25\/6 sin(11\/7-6 t)-47\/6 sin(11\/7-4 t)-86\/5 sin(11\/7-t)+1\/3 sin(2 t+47\/10)+31\/6 sin(3 t+11\/7)+529\/48 sin(5 t+11\/7)+11\/10 sin(8 t+11\/7)+35\/18 sin(9 t+11\/7)+7\/10 sin(11 t+33\/7)+4\/9 sin(12 t+33\/7)+715\/8) theta(79 pi-t) theta(t-75 pi)+(-1\/4 sin(5\/4-12 t)-47\/8 sin(14\/9-9 t)-5\/8 sin(9\/7-8 t)-43\/11 sin(14\/9-4 t)-72\/7 sin(14\/9-3 t)-29\/2 sin(11\/7-2 t)+338\/15 sin(t+11\/7)+5\/7 sin(5 t+11\/7)+5\/7 sin(6 t+11\/7)+2\/5 sin(7 t+37\/8)+13\/3 sin(10 t+8\/5)+19\/18 sin(11 t+14\/3)+67\/7) theta(75 pi-t) theta(t-71 pi)+(292\/5 sin(t+9\/2)+2\/3 sin(2 t+13\/12)+17\/3 sin(3 t+4)+4\/5 sin(4 t+11\/7)+11\/6 sin(5 t+29\/8)+599\/3) theta(71 pi-t) theta(t-67 pi)+(-13\/4 sin(7\/8-2 t)+719\/18 sin(t+21\/11)+14\/3 sin(3 t+13\/8)+33\/32 sin(4 t+4\/3)-83) theta(67 pi-t) theta(t-63 pi)+(216\/7 sin(t+10\/3)+13\/5 sin(2 t+50\/11)+38\/9 sin(3 t+10\/3)+7\/4 sin(4 t+4)+6\/5 sin(5 t+14\/5)-295\/2) theta(63 pi-t) theta(t-59 pi)+(-7\/9 sin(2\/5-7 t)-13\/7 sin(7\/9-5 t)-186\/37 sin(1\/2-3 t)+103\/3 sin(t+3\/7)+15\/2 sin(2 t+5\/8)+14\/15 sin(4 t+1\/16)+1\/3 sin(6 t+26\/7)+323\/7) theta(59 pi-t) theta(t-55 pi)+(302\/7 sin(t+30\/7)+25\/6 sin(2 t+27\/7)-69\/4) theta(55 pi-t) theta(t-51 pi)+(-11\/7 sin(5\/8-10 t)-12\/7 sin(4\/9-4 t)+113\/16 sin(t+23\/11)+307\/7 sin(2 t+17\/7)+7\/3 sin(3 t+17\/9)+7\/5 sin(5 t+4\/9)+35\/6 sin(6 t+1)+5\/8 sin(7 t+8\/7)+26\/27 sin(8 t+33\/7)+4\/7 sin(9 t+10\/7)+3\/7 sin(11 t+2)+497\/5) theta(51 pi-t) theta(t-47 pi)+(-16\/17 sin(1\/5-12 t)-6\/7 sin(5\/6-10 t)-13\/8 sin(5\/6-8 t)-16\/7 sin(1\/3-6 t)-35\/9 sin(3\/5-4 t)+8 sin(t+14\/3)+554\/7 sin(2 t+12\/5)+65\/8 sin(3 t+18\/7)+3 sin(5 t+7\/3)+13\/7 sin(7 t+16\/7)+17\/10 sin(9 t+29\/10)+12\/7 sin(11 t+41\/14)+64\/5) theta(47 pi-t) theta(t-43 pi)+(-5\/8 sin(1\/3-3 t)-11\/3 sin(5\/4-t)+18\/5 sin(2 t+26\/7)+1\/2 sin(4 t+18\/5)+1039\/5) theta(43 pi-t) theta(t-39 pi)+(-2\/5 sin(1\/3-5 t)-6 sin(3\/5-t)+4 sin(2 t+15\/8)+22\/5 sin(3 t+23\/24)+3\/4 sin(4 t+43\/14)+1697\/8) theta(39 pi-t) theta(t-35 pi)+(-33\/13 sin(48\/47-3 t)-61\/15 sin(2\/7-2 t)+56\/11 sin(t+95\/24)+8\/9 sin(4 t+19\/6)+1\/8 sin(5 t+7\/3)+2\/7 sin(6 t+19\/5)+954\/7) theta(35 pi-t) theta(t-31 pi)+(-12\/13 sin(5\/6-3 t)+9 sin(t+13\/4)+9\/7 sin(2 t+27\/11)+1\/3 sin(4 t+7\/5)+1\/3 sin(5 t+17\/6)+1\/6 sin(6 t+3\/8)+1351\/8) theta(31 pi-t) theta(t-27 pi)+(-33\/8 sin(9\/10-3 t)-181\/6 sin(4\/9-t)+36\/7 sin(2 t+1)+7\/9 sin(4 t+8\/5)+4\/5 sin(5 t+85\/21)+797\/4) theta(27 pi-t) theta(t-23 pi)+(-11\/10 sin(11\/8-5 t)-47\/9 sin(3\/4-3 t)-449\/13 sin(2\/7-t)+38\/7 sin(2 t+7\/5)+9\/7 sin(4 t+9\/7)+1436\/7) theta(23 pi-t) theta(t-19 pi)+(494\/3-314\/9 sin(14\/13-t)) theta(19 pi-t) theta(t-15 pi)+(-13\/6 sin(1\/7-2 t)-220\/3 sin(8\/9-t)+554\/5) theta(15 pi-t) theta(t-11 pi)+(521\/5 sin(t+32\/7)+14\/13 sin(2 t+53\/13)+31\/3 sin(3 t+25\/6)+5\/6 sin(4 t+13\/3)+31\/10 sin(5 t+19\/5)+40\/39 sin(6 t+53\/13)+5\/4 sin(7 t+24\/7)+sin(8 t+65\/16)+4\/7 sin(9 t+33\/13)+24\/25 sin(10 t+26\/7)+2\/5 sin(11 t+7\/4)+20\/21 sin(12 t+46\/13)-2527\/10) theta(11 pi-t) theta(t-7 pi)+(-9\/7 sin(2\/9-6 t)-9\/5 sin(7\/9-4 t)-111\/10 sin(2\/7-3 t)-20\/7 sin(4\/3-2 t)-1399\/10 sin(6\/5-t)+26\/7 sin(5 t+8\/7)+13\/4 sin(7 t+11\/5)+26\/25 sin(8 t+1\/6)+35\/12 sin(9 t+17\/6)+5\/7 sin(10 t+1\/2)+29\/14 sin(11 t+23\/7)+1\/3 sin(12 t+6\/11)-1749\/8) theta(7 pi-t) theta(t-3 pi)+(-12\/11 sin(5\/11-37 t)-3\/5 sin(1\/6-35 t)-5\/7 sin(5\/7-33 t)-17\/7 sin(1\/2-32 t)-1\/16 sin(4\/3-29 t)-4 sin(26\/25-27 t)-16\/7 sin(1\/2-21 t)-65\/9 sin(8\/7-20 t)-14\/9 sin(13\/9-18 t)-33\/13 sin(1\/5-17 t)-31\/15 sin(1\/3-14 t)-395\/6 sin(1\/7-5 t)-333\/5 sin(16\/15-4 t)+240 sin(t+22\/5)+639\/16 sin(2 t+12\/5)+247\/2 sin(3 t+1\/3)+331\/10 sin(6 t+11\/6)+331\/8 sin(7 t+11\/6)+161\/6 sin(8 t+7\/6)+114\/5 sin(9 t+3\/7)+3\/8 sin(10 t+14\/9)+88\/7 sin(11 t+7\/6)+76\/5 sin(12 t+32\/9)+26\/5 sin(13 t+16\/11)+285\/26 sin(15 t+67\/33)+22\/5 sin(16 t+1\/9)+5\/8 sin(19 t+11\/5)+29\/7 sin(22 t+2\/3)+31\/9 sin(23 t+5\/2)+37\/12 sin(24 t+1\/9)+18\/7 sin(25 t+2\/7)+28\/9 sin(26 t+3\/5)+5\/6 sin(28 t+20\/9)+15\/7 sin(30 t+27\/8)+18\/7 sin(31 t+1\/2)+3\/8 sin(34 t+68\/23)+11\/6 sin(36 t+35\/8)+4\/3 sin(38 t+40\/9)+15\/8 sin(39 t+29\/14)-341\/7) theta(3 pi-t) theta(t+pi)) theta(sqrt(sgn(sin(t\/2))))

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