不请自来，先安利一波。

pocketCAS，目前发现的iOS上最有逼格的两款数学作图APP之一，另一款是VisualMath4D。贵乎python、mathematica 、matlab和R的大神太多，各种花式爱心函数也层出不穷，但这些PC端的高级语言有个共同缺点：表白时携带不便。还是手机好装X。

虽然pocketCAS的大小只有40M，但在作图方面，它有着自己的优势：不仅可以通过添加参数anim绘制动图，还可以用类C语言脚本自定义函数。

展示几个表达爱意的动图，不定期更新：

Fig. 1

笛卡尔心形线的极坐标方程

//Cardioid R=1,r=1,d=1,(R+r)/r=2

//!x=-4..4,y=-4..4,fixedAspectRatio,noGrid,legendDisplayMode=2

cos(t),sin(t)//!dontDrawSpecialPoints,graphColor=#0000FF

2sin(t*anim/(2π))-sin(2t*anim/(2π)),2cos(t*anim/(2π))-cos(t*2anim/(2π))//!val=0..2π,dontDrawSpecialPoints,graphColor=#FF0000

[cos(t)+2sin(anim),sin(t)+2cos(anim)]//!val=0..2π,graphColor=#0000FF

[[2sin(anim),2sin(anim)-sin(2anim)],[2cos(anim),2cos(anim)-cos(2anim)]]//!graphColor=#FF0000

Fig. 2

//!x=-4.71286..5.25629,y=-4.65963..2.41167,fixedAspectRatio,noGrid

abs(x)-abs(0.5*x+1)-abs(0.5*x-1)+(abs(0.5*x+2)+abs(0.5*x-2)-abs(0.5*x+1)-(abs(0.5*x-1)))*sin(5*π*x+8*anim)//!dontDrawSpecialPoints,graphColor=#FF0000

Fig. 3

//!x=-20..20,y=-20..20,fixedAspectRatio,noGrid

16(sin(t*(anim/(2π))))^3,13cos(t*(anim/(2π)))-5cos(2t*(anim/(2π)))-2cos(3t*(anim/(2π)))-cos(4t*(anim/(2π)))//!val=0..2π,dontDrawSpecialPoints,graphColor=#FF0000

[4(sin(anim))^3,16*(sin(anim))^3],[0,13*cos(anim)-5*cos(2*anim)-2*cos(3*anim)-cos(4*anim)]]//dontDrawSpecialPoints,graphColor=#FF0000//!dontDrawSpecialPoints,graphColor=#FF0000

[[0,4(sin(anim))^3],[5,0]]//dontDrawSpecialPoints,graphColor=#FF0000//!dontDrawSpecialPoints,graphColor=#FF0000

Fig. 4

//!x=-5..5,anim=0..20,animStep=2π/200,fixedAspectRatio,noGrid

x^(2/3)+0.9*sin(anim*π*x)*√(3.3x^2)//!dontDrawSpecialPoints,graphColor=#FF0000

(-x)^(2/3)+0.9*sin(anim*π*(-x))*√(3.3-(-x)^2)//!dontDrawSpecialPoints,graphColor=#FF0000

Fig. 5

这个比较污，原函数来自日本高校欧派函数(おっぱい関数)对抗大赛中的作品。

//!x=-1.94367..7.33127,y=0.227793..7.18399,fixedAspectRatio,noGrid

2.09*exp(1.16*t+0.1cos(anim))*cos(1.16*t)+exp(-(t-0.615)^2/0.002592-0.06*cos(anim))/3.1797,1.31*exp(1.31*t)*sin(0.885*t)//!val=-0.5π..π,dontDrawSpecialPoints

怦然心动大概就是这样吧。