This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Thanks, gold 20Aug2020
Here are TCL calculations on the Collatz Sequences.
The collatz_sequence proc returns the collatz_sequence from positive integers. This program can easily generate an endless loop. The iteration number is a stop or limit to iteration. By custom, the end of collatz_sequence is 1 or start of repetition.
if $N even, return { $N / 2 }. If $N odd, return (3*$N+1). Continue the collatz_sequence until returned item is 1 or start of repetition.
In planning any software, it is advisable to gather a number of testcases to check the results of the program.
table, Partial Collatz_Sequences | printed in | TCL format | |
---|---|---|---|
number | iteration | partial Collatz_Sequences | comment, if any |
3 | 5 | 3 10 5 16 8 4 2 1 | |
4 | 5 | 4 2 1 | |
5 | 5 | 5 16 8 4 2 1 | |
6 | 5 | 6 3 10 5 16 8 4 2 | |
7 | 5 | 7 22 11 34 17 52 26 13 40 | |
8 | 5 | 8 4 2 1 | |
9 | 5 | 9 28 14 7 22 11 34 17 52 | |
10 | 5 | 10 5 16 8 4 2 1 | |
11 | 5 | 11 34 17 52 26 13 40 20 | |
12 | 5 | 12 6 3 10 5 16 8 4 | |
13 | 5 | 13 40 20 10 5 16 8 | |
14 | 5 | 14 7 22 11 34 17 52 26 13 40 | |
15 | 5 | 15 46 23 70 35 106 53 160 80 | |
16 | 5 | 16 8 4 2 1 | |
17 | 5 | 17 52 26 13 40 20 10 | |
18 | 5 | 18 9 28 14 7 22 11 34 17 52 | |
19 | 5 | 19 58 29 88 44 22 11 34 | |
20 | 5 | 20 10 5 16 8 4 2 |
# pretty print from autoindent and ased editor # Collatz_Sequences (3*N+1) in Console Example Demo for TCL V2 # Console program example demo # written on Windows 10 on TCL # working under TCL version 8.6 # gold on TCL Club , 11sep2021 package require Tk package require math::numtheory package require math::constants package require math::trig package require math namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory math::trig math::constants } set tclprecision 17 ;# logic tests for even, odd, positive, negative, conditions of positive numbers ;# uses logic inside expr , if positive return 1, if not positive return 0 proc isPositive x {return [ expr {$x>0}]} ;# Richard Suchenwirth RS idea in Math Sugar ;# uses logic inside expr, if negative return 1, if not negative return 0 proc isNegative x { return [ expr {$x<0}]} ;# Richard Suchenwirth RS idea from wiki: Math Sugar ;# idea by Michael Barth ;# No error traps or safety nets here for negative and real numbers. ;# conditional proc IsOdd, if N odd, return 1, if N not odd, return 0. proc IsOdd { N } { return [ expr {$N % 2} ] } ;# Usage IsOdd 5 ;# returns 1 ;# conditional proc IsEven, if N even, return 1. If N not even return 0. proc IsEven { N } { return [ expr { ( $N + 1 ) % 2} ] } IsEven 4 ;# returns 1 ;# ;# Results: collatz_sequence ;# ;# Return the collatz_sequence from positive integer ;# ;# Arguments: ;# number first value is number ;# iteration second value is iteration ;# ;# ;# Note: This program can easily generate an endless loop. ;# iteration number is a stop or limit to iteration ;# By custom, the end of collatz_sequence is 1 or start of repetition proc collatz_sequence {number iteration} { set sequence [ list ] set count 0 set val $number set skip 0 lappend sequence $val while {$count < $iteration} { if { $val == $skip } { lappend sequence 1 ; break } if { [ IsEven $val ] } { set val [ expr { $val / 2 } ] ; lappend sequence $val } if { [ IsOdd $val ] } { set val [ expr { (3 * $val ) + 1 } ]; lappend sequence $val } incr count if { $count == $iteration } { break } set skip 2 } return $sequence } console show puts " Console wrapper for solution proc" puts " ***************************" puts " ***************************" puts "collatz_sequence 31 15 collatz_sequence [collatz_sequence 31 15]" puts "collatz_sequence 11 15 collatz_sequence [collatz_sequence 11 15]" puts "collatz_sequence 10 15 collatz_sequence [collatz_sequence 10 15]" puts "collatz_sequence 9 15 collatz_sequence [collatz_sequence 9 15]" puts "collatz_sequence 8 15 collatz_sequence [collatz_sequence 8 15]" puts "collatz_sequence 7 15 collatz_sequence [collatz_sequence 7 15]" puts "collatz_sequence 6 15 collatz_sequence [collatz_sequence 6 15]" puts "collatz_sequence 5 15 collatz_sequence [collatz_sequence 5 15]" puts "collatz_sequence 4 15 collatz_sequence [collatz_sequence 4 15]" puts "collatz_sequence 3 15 collatz_sequence [collatz_sequence 3 15]" proc table_format_out n { set sum 0 # initial level set count 1 puts "%| table| | printed in|TCL format |% " puts "%| number | iteration |partial Collatz_Sequences |comment, if any|% " # adapted proc from <RS> # printout in TCL WIKI format table for { set i 1 } { $i <= $n } { incr i } { incr count puts "&| $count | 5 | [ collatz_sequence $count 5 ]| |&" incr sum $i } return $sum } table_format_out 31 # following dresses up console output to easy eye # end of working deck # add cosmetics below to bottom of file console eval {.console config -bg palegreen} console eval {.console config -font {fixed 20 bold}} console eval {wm geometry . 40x20} console eval {wm title . " Report for Collatz_Sequences (3*N+1) Calculator V2 "} console eval {. configure -background orange -highlightcolor brown -relief raised -border 30}
Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Thanks, gold 12Aug2020
x
Category Numerical Analysis | Category Toys | Category Calculator | Category Mathematics | Category Example | Toys and Games | Category Games | Category Application | Category GUI |