\startbuffer[UDBasic]

pair A,B,C,D;

pair E, F, G, H;

path p,q;

numeric ang,maxNum;

u:=3D1in;

= A=3D(.95*TextWidth,u); B=3D(0,u); C=3D(0,0); D=3D(.95*TextWidth,0);

p :=3D A--B--C--D;

q :=3D (TextWidth,1.5u)--(0,1.5u)--(0,-.5u)--(TextWidth,-.5u)--cycle;

z0=3D(.1u,0);

= vardef nextPt (expr = M,N) =3D

= if ypart(N) =3D 0:

H :=3D whatever[N, N + dir(.5*angle(M-N))*u] = =3D whatever[A,B];

else:

H :=3D= whatever[N, N + dir(.5*angle(M-N))*u] = =3D whatever[C,D];

fi;

enddef;

def grayUD(expr i) =3D

draw G -- if ypart(B)=3Dypart(G): = B -- C else: C -- B fi --z[i];

filldraw z[i]+2*(G-z[i])*u= -- z[i] -- z[i+1] = -- z[i+1]+(G-z[i])*u= -- cycle withcolor = .75white;

draw G -- z[i+1] = dashed evenly;

draw z[0] for k=3D0 upto i: --z[k] = endfor dashed evenly;

clip currentpicture to = q;

setbounds currentpicture to boundingbox = q;

enddef;

= def linesUD(expr = i) =3D

draw = p;

draw z0 for k=3D0 upto i+1: --z[k] = endfor dashed evenly;

setbounds = currentpicture to boundingbox q;

= enddef;

\stopbuffer

\startbuffer[UDpts]

ang :=3D 40;

z[1] =3D whatever[z[0], = z[0]+dir(ang)*u] = =3D whatever[A,B];

G :=3D whatever[z[0], z[0]+dir(2*ang)*u] = =3D whatever[A,B];

for k =3D 2 upto 20:

z[k] = =3D nextPt(z[k-2],z[k-1]);

maxNum :=3D k;

= exitif xpart(z[k]) > TextWidth;

= endfor;

\stopbuffer

\startbuffer[UD0]

draw p;

= setbounds currentpicture to boundingbox q;

\stopbuffer

\startbuffer[UD1]

grayUD(0);

\stopbuffer

\startbuffer[UD11]

linesUD(0);

\stopbuffer

\startbuffer[UD2]

G :=3D z0;

grayUD(1)

\stopbuffer

\startbuffer[UD21]

linesUD(1);

\stopbuffer

\startbuffer[UD3]

G :=3D z1;

grayUD(2);

\stopbuffer

\startbuffer[UD31]

linesUD(2);

\stopbuffer

\startbuffer[UD4]

G :=3D z2;

grayUD(3);

\stopbuffer

\startbuffer[UD41]

linesUD(3);

\stopbuffer

\startbuffer[UD5]

G :=3D z3;

grayUD(4);

\stopbuffer

\startbuffer[UD51]

linesUD(4);

\stopbuffer

\startbuffer[UDFinal]

draw p;

draw= z0--z1--z2--z3--z4--z5--z6--z7--z8 dashed evenly;

setbounds = currentpicture to boundingbox q;

\stopbuffer

\setupinteraction[state=3Dstart]

\usemodule[animation]

\starttext

\startanimation[menu=3Dyes]

{\processMPbuffer[UDBasic,UDpts,UD0]}

{\processMPbuffer[UDBasic,UDpts,UD1]}

{\processMPbuffer[UDBasic,UDpts,UD11]}

{\processMPbuffer[UDBasic,UDpts,UD2]}

{\processMPbuffer[UDBasic,UDpts,UD21]}

{\processMPbuffer[UDBasic,UDpts,UD3]}

{\processMPbuffer[UDBasic,UDpts,UD31]}

{\processMPbuffer[UDBasic,UDpts,UD4]}

{\processMPbuffer[UDBasic,UDpts,UD41]}

{\processMPbuffer[UDBasic,UDpts,UD5]}

{\processMPbuffer[UDBasic,UDpts,UD51]}

{\processMPbuffer[UDBasic,UDpts,UDFinal]}

\stopanimation

\stoptext

\startMPinitializations%{UDBasic}

pair A,B,C,D;

pair E, F, G, H;

path = p,q;

numeric ang,maxNum;

numeric n; %AM Added

u:=3D1in;

A=3D(.95*TextWidth,u); B=3D(0,u); = C=3D(0,0); D=3D(.95*TextWidth,0);

p :=3D A--B--C--D;

= q :=3D (TextWidth,1.5u)--(0,1.5u)--(0,-.5u)--(TextWidth,-.5u)--cycle;

z0=3D(.1u,0);

= vardef= nextPt (expr = M,N) =3D

= if = ypart(N) = =3D 0:

H :=3D whatever[N, N + dir(.5*angle(M-N))*u] = =3D whatever[A,B];

else:

H :=3D whatever[N, N + dir(.5*angle(M-N))*u] = =3D whatever[C,D];

fi;

= H

enddef;

= def = grayUD(expr = i) =3D

draw G = -- = if = ypart(B)=3Dypart(G): = B -- = C else: = C -- = B fi = --z[i];

filldraw z[i]+2*(G-z[i])*u = -- = z[i] -- z[i+1] = -- = z[i+1]+(G-z[i])*u = -- = cycle = withcolor .75white;

draw G -- z[i+1] = dashed= evenly;

draw z[0] = for = k=3D0 upto i: --z[k] = endfor= dashed evenly;

clip currentpicture to q;

= enddef;

def = linesUD(expr = i) =3D

draw = p;

draw z0 for k=3D0 = upto = i+1: --z[k] = endfor= dashed evenly;

= % AM: removed. Set in in = the main code

% setbounds currentpicture to boundingbox = q;

enddef;

ang :=3D 40;

z[1] = =3D whatever[z[0], = z[0]+dir(ang)*u] = =3D whatever[A,B];

% AM: Changed next line from G to = z[-1]

z[-1] = =3D whatever[z[0], = z[0]+dir(2*ang)*u] = =3D whatever[A,B];

for k =3D 2 upto 20:

z[k] =3D = nextPt(z[k-2],z[k-1]);

maxNum :=3D k;

= exitif xpart(z[k]) = > = TextWidth;

endfor;

\stopMPinitializations

\startuseMPgraphic{foldUD}{num}

numeric n;

n :=3D = \MPvar{num}-1;

G :=3D z[n-1];

grayUD(n);

\stopuseMPgraphic

\startuseMPgraphic{dotLines}{num}

numeric n;

n :=3D = \MPvar{num}-1;

linesUD(n);

\stopuseMPgraphic

\setupinteraction[state=3Dstart]

\usemodule[animation]

\starttext

\startanimation[menu=3Dyes]

\dorecurse{7}

{

{\useMPgraphic{foldUD}{num=3D\recurselevel}}

{\useMPgraphic{dotLines}{num=3D\recurselevel}}

}

\stopanimation

\stoptext