#!/bin/bash
#Usage script [branch_size] [depth]
#example ./script 10 4 ./script 77 7
pad=$(printf "_%.0s" {1..500})

create_fractal_pattern() {
    local left_length=${1}
    local right_length=${2}
    local branch_size=${3}
    local depth=${4}

    if [[ ${depth} == 0 ]]
    then
        return
    fi

    paste -d "" <( create_fractal_pattern $(( left_length - branch_size )) ${branch_size} $(( branch_size / 2 )) $(( depth - 1 )) ) \
        <( create_fractal_pattern $(( branch_size - 1 )) $(( right_length - branch_size )) $(( branch_size / 2 )) $(( depth - 1 )) )

    for (( i=${branch_size}-1; i>=0; i-=1 ))
    do
        printf "%s1%s1%s\n" "${pad:1:left_length-i-1}" "${pad:1:i*2+1}" "${pad:1:right_length-i-1}"
    done

    for (( i=0; i<${branch_size}; i+=1 ))
    do
        printf "%s1%s\n" ${pad:1:left_length} ${pad:1:right_length}
    done
}

compute_max_width() {
    local branch_size=${1}
    local depth=${2}
    local res=0
    for (( i=0; i<depth; ++i ))
    do
        res=$(( res + branch_size ))
        branch_size=$(( branch_size / 2 ))
    done
    echo $(( res * 2 + 7 ))
}

draw_fractal() {
    local branch_size=${1}
    local depth=${2}
    local width=$(compute_max_width ${branch_size} ${depth})
    local left_bound=$(( (width + 1) / 2 -1 ))
    local right_bound=$(( width / 2 ))
    printf "%s\n" ${pad:1:width}
    create_fractal_pattern ${left_bound} ${right_bound} ${branch_size} ${depth}
}

draw_fractal ${1} ${2} | tr ' ' '\n'