mirror of https://github.com/tLDP/LDP
70 lines
1.7 KiB
Bash
70 lines
1.7 KiB
Bash
#!/bin/bash
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# collatz.sh
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# The notorious "hailstone" or Collatz series.
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# -------------------------------------------
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# 1) Get the integer "seed" from the command-line.
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# 2) NUMBER <-- seed
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# 3) Print NUMBER.
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# 4) If NUMBER is even, divide by 2, or
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# 5)+ if odd, multiply by 3 and add 1.
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# 6) NUMBER <-- result
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# 7) Loop back to step 3 (for specified number of iterations).
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#
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# The theory is that every such sequence,
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#+ no matter how large the initial value,
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#+ eventually settles down to repeating "4,2,1..." cycles,
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#+ even after fluctuating through a wide range of values.
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#
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# This is an instance of an "iterate,"
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#+ an operation that feeds its output back into its input.
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# Sometimes the result is a "chaotic" series.
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MAX_ITERATIONS=200
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# For large seed numbers (>32000), try increasing MAX_ITERATIONS.
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h=${1:-$$} # Seed.
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# Use $PID as seed,
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#+ if not specified as command-line arg.
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echo
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echo "C($h) -*- $MAX_ITERATIONS Iterations"
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echo
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for ((i=1; i<=MAX_ITERATIONS; i++))
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do
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# echo -n "$h "
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# ^^^
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# tab
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# printf does it better ...
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COLWIDTH=%7d
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printf $COLWIDTH $h
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let "remainder = h % 2"
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if [ "$remainder" -eq 0 ] # Even?
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then
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let "h /= 2" # Divide by 2.
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else
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let "h = h*3 + 1" # Multiply by 3 and add 1.
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fi
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COLUMNS=10 # Output 10 values per line.
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let "line_break = i % $COLUMNS"
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if [ "$line_break" -eq 0 ]
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then
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echo
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fi
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done
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echo
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# For more information on this strange mathematical function,
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#+ see _Computers, Pattern, Chaos, and Beauty_, by Pickover, p. 185 ff.,
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#+ as listed in the bibliography.
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exit 0
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