BASH: Create matrix for Y Tree ASCII shape

tree.sh

#!/bin/bash
read n;
declare -A matrix
num_rows=63
num_columns=100

for ((i=1;i<=num_rows;i++)) do
  for ((j=1;j<=num_columns;j++)) do
    matrix[$i,$j]="_";
  done
done

function drawTree() {
  local x=$1;
  local y=$2;
  local depth=$3;
  local height=$4;

  if [ $depth -eq 0 ]; then
    return 1;
  fi 
  local hh=$((height/2));
  for ((i=1;i<=hh;i++)) do
    matrix[$(($y+$i)),$x]="1";
    matrix[$(($y+$hh+$i)),$(($x-$i))]="1";
    matrix[$(($y+$hh+$i)),$(($x+$i))]="1";
  done
  drawTree $((x-hh)) $((y+height)) $((depth-1)) $hh;
  drawTree $((x+hh)) $((y+height)) $((depth-1)) $hh;
}

drawTree 50 0 $n 32

for ((i=num_rows;i>=0;i--)) do
  for ((j=1;j<=num_columns;j++)) do
    printf '%s' "${matrix[$i,$j]}";
  done
  printf '\n';
done