#!/bin/bash
# collatz.sh

#  The notorious "hailstone" or Collatz series.
#  -------------------------------------------
#  1) Get the integer "seed" from the command line.
#  2) NUMBER <-- seed
#  3) Print NUMBER.
#  4)  If NUMBER is even, divide by 2, or
#  5)+ if odd, multiply by 3 and add 1.
#  6) NUMBER <-- result 
#  7) Loop back to step 3 (for specified number of iterations).
#
#  The theory is that every sequence,
#+ no matter how large the initial value,
#+ eventually settles down to repeating "4,2,1..." cycles,
#+ even after fluctuating through a wide range of values.
#
#  This is an instance of an "iterate,"
#+ an operation that feeds its output back into its input.
#  Sometimes the result is a "chaotic" series.


MAX_ITERATIONS=200
# For large seed numbers (>32000), try increasing MAX_ITERATIONS.

h=${1:-$$}                      #  Seed.
                                #  Use $PID as seed,
                                #+ if not specified as command-line arg.

echo
echo "C($h) --- $MAX_ITERATIONS Iterations"
echo

for ((i=1; i<=MAX_ITERATIONS; i++))
do

# echo -n "$h	"
#            ^^^ 
#            tab
# printf does it better ...
COLWIDTH=%7d
printf $COLWIDTH $h

  let "remainder = h % 2"
  if [ "$remainder" -eq 0 ]   # Even?
  then
    let "h /= 2"              # Divide by 2.
  else
    let "h = h*3 + 1"         # Multiply by 3 and add 1.
  fi


COLUMNS=10                    # Output 10 values per line.
let "line_break = i % $COLUMNS"
if [ "$line_break" -eq 0 ]
then
  echo
fi  

done

echo

#  For more information on this strange mathematical function,
#+ see _Computers, Pattern, Chaos, and Beauty_, by Pickover, p. 185 ff.,
#+ as listed in the bibliography.

exit 0