y_shape.sh

#!/bin/bash

TREE_SECTION_LENGTH=16
COLS=100
ROWS=63
idx=0
CURRENT_SEC_LENGTH=${TREE_SECTION_LENGTH}

declare -a BRANCH_POSITIONS
BRANCH_POSITIONS[1]=$(expr ${COLS} / 2 - 1)

declare -A GRID
for (( i=0 ; i<${ROWS} ; i++ ))
do
    for (( j=0 ; j<${COLS} ; j++ ))
    do
        GRID[${i},${j}]="_"
    done
done

# n from 1 to 5 inclusive.
read n
n_max=$(expr ${n} - 1)

for (( n=0 ; n<=${n_max} ; n++ ))
do
  CURRENT_SEC_LENGTH=$(echo "${TREE_SECTION_LENGTH} / 2^${n}" | bc)
  for (( i=1 ; i<=${CURRENT_SEC_LENGTH} ; i++ ))
  do
    for (( j=0 ; j<=${#BRANCH_POSITIONS[*]} ; j++ ))
    do
      GRID[${idx},${BRANCH_POSITIONS[j]}]=1
    done
    idx=$((idx + 1))
  done

  BRANCH_POSITIONS=($(echo ${BRANCH_POSITIONS[*]} ${BRANCH_POSITIONS[*]} | tr " " "\n" | sort -g | xargs))

  for (( i=1 ; i<=${CURRENT_SEC_LENGTH} ; i++ ))
  do
    OFFSET=-1
    for (( j=0 ; j<${#BRANCH_POSITIONS[*]} ; j++ ))
    do
      BRANCH_POSITIONS[j]=$((${BRANCH_POSITIONS[j]} + ${OFFSET}))
      OFFSET=$((${OFFSET} * -1))
    done
    for (( j=0 ; j<${#BRANCH_POSITIONS[*]} ; j++ ))
    do
      GRID[${idx},${BRANCH_POSITIONS[j]}]=1
    done
    idx=$((idx+ 1))
  done
done

for (( i=$(expr ${ROWS} - 1) ; i>=0 ; i-- ))
do
  for (( j=0 ; j<${COLS} ; j++ ))
  do
    printf ${GRID[$i,$j]}
  done
  echo
done