Implementation of cantor set without recursion

Question

I'm working on the implementation of a cantor set on a 2-dimensional plane. It looks like this. Honestly, There is the obvious algorithm for the cantor set, but it includes a recursive method call. Unfortunately, My environment(Houdini vex) does not support recursive function calls, so I have to design the algorithm without using recursion.

1. Is it possible to represent a cantor set without recursion?
2. How can I represent the recursive thing in the algorithm without recursion?

Cantor set implementation on a 2-dimensional grid

int size=ch("size"); //size=27
int can[]={0};
int offset=0;
int col=size;
append(can,size);
int index=0;
int step=1;
int temp[]={};
int firstentry=0;
function void line(int x1; int x2)
{
 //this function gets x1(startpoint), x2(endpoint) and color entries in
 int step= x2-x1;
 if (step==0)
 {
 
 
 //color the single sqaure 
 setprimgroup(0,"cantor",x1,1,"set");
 }
 else{
 //setprimgroup do the role of coloring the squre.
 
 for(int i=x1; i<=step+x1; i++)
 {
 setprimgroup(0,"cantor",i,1,"set");
 }
 }
 
}
while(size>=1)
{
 //first step 0~26
 if(index<size)
 {
 //first line is set.
 setprimgroup(0,"cantor",index,1,"set");
 index+=1;
 
 //first entry indicates the first entry of the row.
 
 }
 
///
 else{
 //split by 1/3
 //first entry indicates the first entry of the row.
 firstentry+=col;
 size=size/3;
 step=step*2;
 //done only for subdivision ex 1,2,4...
 for(int i=0; i<step; i++)
 {
 
 offset = size*2;
 int start=index;
 int end= start+size-1;
 
 line(start,end);
 
 
 printf("start %g end %g \n",start,end);
 
 index+=offset;
 //
 }
 
 index=firstentry+col;
 
 //for recursive step, multiply by 2.
 
 
 }
 
}

this language resembles C, I don't want you to do coding for me. Please present just an idea for correcting the gap calculation.

Answer 1

Yes. It can be expressed without recursion, as long as you have loops and data structures. Any recursive algorithm can be converted to a non-recursive iterative algorithm, by introducing an explicit stack. See, e.g., Iteration can replace Recursion?, Iterative and/or tail-recursive implementations of merge sort?, Do we need recursion in programming language to solve any problem?.