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

> restart:

> x1:=cos(t):

> y1:=sin(t):

> r:=sqrt(2-2*cos(t)):

> t:=n*2*Pi/100:

> plot([[x1+r*cos(s),y1+r*sin(s),s=0..2*Pi]$n=1..100],scaling=constrained,axes=none,color=green);

> restart:

> x1:=cos(t):

> y1:=sin(t):

> r:=abs(x1):

> t:=n*2*Pi/100:

> plot([[x1+r*cos(s),y1+r*sin(s),s=0..2*Pi]$n=1..100],scaling=constrained,axes=none,color=green);

> restart:

> t:=n*2*Pi/50:

> x0:=cos(t):

> y0:=sin(t):

> x1:=2*cos(t)/3+cos(2*t)/3:

> y1:=2*sin(t)/3-sin(2*t)/3:

> r:=sqrt((x0-x1)^2+(y0-y1)^2):

> plot([[x0+r*cos(s),y0+r*sin(s),s=0..2*Pi]$n=0..100],scaling=constrained,axes=none,color=green);

> restart:

> t:=n*2*Pi/50:

> x0:=cos(t):

> y0:=sin(t):

> x1:=3*cos(t)/4+cos(3*t)/4:

> y1:=3*sin(t)/4-sin(3*t)/4:

> r:=sqrt((x0-x1)^2+(y0-y1)^2):

> plot([[x0+r*cos(s),y0+r*sin(s),s=0..2*Pi]$n=0..100],scaling=constrained,axes=none,color=green);

> restart:

> x1:=cos(t):

> y1:=sin(t):

> m:=[x1+t*sin(s),y1+t*cos(s),s=-Pi..Pi]:

> t:=n*Pi/20:

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

> 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,numpoints=100);

>