Dear Hans,

Your code works fine.

\starttext

\startMPcode
   numeric maxCount;
   maxCount := 10;
   setglobalmacro("MyMacro",decial maxCount);
   setglobalcount("MyCount",maxCount);
\stopMPcode


\dorecurse{\MyMacro}{It is \recurselevel. }\par
\dorecurse{\MyCount}{It is \recurselevel. }\par

\stoptext

I applied your method to my code as following. 

\newcount\udCount %%% add count
\startMPinitializations%{UDBasic}
pair A,B,C,D;
pair E, F, G, H;
path p,q;
numeric ang,maxNum;

numeric n; %AM Added

u:=1in;
A=(.95*TextWidth,u); B=(0,u); C=(0,0); D=(.95*TextWidth,0);
p := A--B--C--D;
q := (TextWidth,1.5u)--(0,1.5u)--(0,-.5u)--(TextWidth,-.5u)--cycle;
z0=(.1u,0);
vardef nextPt (expr M,N) =
if ypart(N) = 0:
H := whatever[N, N + dir(.5*angle(M-N))*u] = whatever[A,B];
else:
H := whatever[N, N + dir(.5*angle(M-N))*u] = whatever[C,D];
fi;
H
enddef;

def grayUD(expr i) =
draw G -- if ypart(B)=ypart(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=0 upto i: --z[k] endfor dashed evenly;
clip currentpicture to q;
enddef;

def linesUD(expr i) =
draw p;
draw z0 for k=0 upto i+1: --z[k] endfor dashed evenly;

% AM: removed. Set in in the main code
% setbounds currentpicture to boundingbox q;
enddef;

ang := 40;
z[1] = whatever[z[0], z[0]+dir(ang)*u] = whatever[A,B];

% AM: Changed next line from G to z[-1]
z[-1] = whatever[z[0], z[0]+dir(2*ang)*u] = whatever[A,B];
for k = 2 upto 20:
z[k] = nextPt(z[k-2],z[k-1]);
maxNum := k;
exitif xpart(z[k]) > TextWidth;
endfor;
maxNum := maxNum-1;
setglobalmacro("udMacro",decimal maxNum); %%% define udMacro and udCount
setglobalcount("udCount",maxNum);

\stopMPinitializations

\startuseMPgraphic{foldUD}{num}
numeric n;
n := \MPvar{num}-1;
G := z[n-1];
grayUD(n);
\stopuseMPgraphic
\startuseMPgraphic{dotLines}{num}
numeric n;
n := \MPvar{num}-1;
linesUD(n);
\stopuseMPgraphic

\setupinteraction[state=start]
\usemodule[animation]
\starttext
%\startanimation[menu=yes]
%{
\dorecurse{\udCount}
{\useMPgraphic{foldUD}{num=\recurselevel}}
{\useMPgraphic{dotLines}{num=\recurselevel}}
%}
%\stopanimation
\stoptext

1. Using “udCount” doesn’t issue error message, but it draws the path p only.
2. Using “udMacro” issue the error message.

Is there anything that I miss?

Best regards,

Dalyoung

**********
tex error       > tex error on line 75 in file /Users/graph/Library/Mobile Documents/com~apple~CloudDocs/texMain/funmath/foldBandMPnew.tex: Undefined control sequence

<argument> \udMacro 
    
<macro> \dorecurse #1->\ifcase #1
    \relax \expandafter \gobbletwoarguments \or \expandafter \syst_helpers_recurse_y \else \expandafter \syst_helpers_recurse_x \fi {#1}
<line 3.75> \dorecurse{\udMacro}
    
65        numeric n;
66        n := \MPvar{num}-1;
67        linesUD(n);
68     \stopuseMPgraphic
69     
70     \setupinteraction[state=start]
71     \usemodule[animation]
72     \starttext
73     %\startanimation[menu=yes]
74     %{
75 >>  \dorecurse{\udMacro}
76      {\useMPgraphic{foldUD}{num=\recurselevel}}
77      {\useMPgraphic{dotLines}{num=\recurselevel}}
78     %}