Construct this pretty flower :

> plot((1+cos(3*t)+sin(3*t)^2),t=0..2*Pi,coords=polar,axes=none,scaling=constrained);

Contruct the line segment s joining (cos(t),0) with (0,sin(t)) as t ranges over [0,2 ]

> x:=cos(t);

> y:=sin(t);

> m:=[[x,0],[0,y]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=red,scaling=constrained,axes=none);

Construct the velocity vector field along a constant motion around a circle

> restart;

> x:=cos(t);

> y:=sin(t);

> m:=[[x,y],[x-y,y+x]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=red,scaling=constrained,axes=none);

Construct this figure

> restart;

> x:=cos(t);

> y:=sin(t);

> m:=[[x,y],[x-t*y,y+t*x]];

> t:=n*Pi/50;

> plot([m$n=1..100],color=red,scaling=constrained,axes=none);

Construct the line segments joining [cos(t),sin(t)] with [cos(2t),sin(2t)] as t ranges over [0,2 ]

> restart;

> x1:=cos(t);

> y1:=sin(t);

> x2:=cos(2*t);

> y2:=sin(2*t);

> m:=[[x1,y1],[x2,y2]];

> t:=k*Pi/50;

> plot([m$k=1..100],color=red,scaling=constrained,axes=none);

Construct this figure

> restart;

> x1:=cos(t);

> y1:=sin(t);

> x2:=cos(3*t);

> y2:=sin(3*t);

> m:=[[x1,y1],[x2,y2]];

> t:=k*Pi/50;

> plot([m$k=1..100],color=red,scaling=constrained,axes=none);

Construct this graph associated with the logistic equation with a=3.7

> x:=0.7;

> a:=3.7;

> y:=a*x*(1-x);

> m:=[];

> for k to 100 do m:=[op(m),[x,x],[x,y]]:x:=y:y:=a*x*(1-x):od:

> plot(m,scaling=constrained);

>

Draw 20 concentric circles as thus:

> restart;

> x:=r*cos(t);

> y:=r*sin(t);

> m:=[x,y,t=0..2*Pi];

> plot([m$r=1..20],color=red,scaling=constrained,axes=none);

Construct the circles with center at (cos(t),sin(t)) passing through the point (1,0) with t ranging over [0,2 ]

> restart;

> x:=cos(t);

> y:=sin(t);

> r:=(2-2*x)^(1/2);

> m:=[x+r*sin(s),y+r*cos(s),s=0..2*Pi];

> t:=n*Pi/50;

> plot([m$n=1..100],color=red,axes=none,scaling=constrained);

Construct the circles with center at (cos(t),sin(t)) and tangent to the y-axis with t ranging over [0,2 ]

> restart;

> x:=cos(t);

> y:=sin(t);

> r:=abs(x);

> m:=[x+r*sin(s),y+r*cos(s),s=-Pi..Pi];

> t:=n*Pi/50;

> plot([m$n=1..100],color=red,axes=none,scaling=constrained);

Construct the circles with center at (cos(t),sin(t)) and passing through (2cos(t)/3+cos(2t)/3,2sin(t)/3+sin(2t)/3) with t ranging over [0,2 ]

> restart;

> x:=cos(t);

> y:=sin(t);

> x1:=2/3*x+1/3*cos(2*t);y1:=2/3*y-1/3*sin(2*t);

> r:=((x-x1)^2+(y-y1)^2)^(1/2);

> m:=[x+r*sin(s),y+r*cos(s),s=0..2*Pi];

> t:=n*Pi/50;

>

> plot([m$n=1..100],color=red,axes=none,scaling=constrained);

Construct this figure:

> restart;

> x:=cos(t);

> y:=sin(t);

> x1:=3/4*x+1/4*cos(3*t);y1:=3/4*y-1/4*sin(3*t);

> r:=((x-x1)^2+(y-y1)^2)^(1/2);

> m:=[x+r*sin(s),y+r*cos(s),s=0..2*Pi];

> t:=n*Pi/50;

>

> plot([m$n=1..100],color=red,axes=none,scaling=constrained);

Construct this pattern:

> restart;

> x:=cos(t);

> y:=sin(t);

> m:=[x+t*sin(s),y+t*cos(s),s=0..2*Pi];

> t:=n*Pi/20;

> plot([m$n=1..100],color=red,axes=none,scaling=constrained);

Construct the reflections of a light ray inside a square :

> restart;

> m:=1.7123:x:=0:y:=0:v:=[[x,y]]:

> for k to 100 do xx:=floor(x)+1:yy:=floor(y)+1:if (yy-y)>m*(xx-x) then x:=xx:y:=m*x else y:=yy:x:=y/m:fi: v:=[op(v),[1-abs(x-2*floor(x/2)-1),1-abs(m*x-2*floor(m*x/2)-1)]] od:

> plot(v,scaling=constrained);

>