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 30Apr2021
gold Here are some calculations on time fractal windows. This calculator uses golden ratio proportions to predict time windows or time fractals of similar probable occurrences based a seed time or initial age decimal years. There is plenty of uncertainty about probable occurrences events after the seed time in decimal years, but the the probable occurrences are largely based on growth, accumulation, and succession following the golden ratio proportions. Not all events in time have golden ratio proportions.
The golden ratio constant is 1.6180339887… As used in the TCL program, the golden ratio conjugate is 0.6180339887… In some circles, a peak is considered 1.6X and a dip is considered 0.6X. The most commonly used Fibonacci ratios as dips include the 23.6%, 38.2%, 50%, 61.8%, and 78.6% shorts. A version of 61.8% is loaded in the TCL program as 0.618... Not sure these Fibonacci ratios apply on all occasions, but there is considerable interest in predicting peaks and dips in Bitcoin cryptocurrency.
#; derivation of analyst Fibonacci constants set $g_constant1 1.61803398874989484820 set result [ expr { 1./ ($g_constant1 * $g_constant1 ) }] #; result out = 2.6180339887498945 set g_constant2 1.61803398874989484820 expr { 1./ ($g_constant * $g_constant ) } #; result out = 0.38196601125010515
The golden time point in any duration is defined 61.8% in its entire length of time. Golden time segments may defined as multiple and alternating time segments in proportion to Fibonacci series constants. An example is 3:2:5:2 (here, 4 time segments approximating golden ratio equivalence 1.618:1:1.618:1). The reported testcase is roughly 3:2:2:5.
The TCL calculator seems to be working as it stands and matches the scanty textbook examples. The calculator carries the numbers out to the TCL 8.6 maximum (17 places), but suggest there is about a 5 per cent accuracy inherent in most inputs and the probable event outputs. One relative error calculation in TCL notation was vis expr {(1 -(28.797 / 27.506))* 100. } >> 4.69 accuracy no units.
#pseudocode can be developed from rules of thumb. #pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude #pseudocode: enter quantity1, quantity2, quantity3 and expected output (quantity4) for testcases. #pseudocode: enter time in years, number of remaining items #pseudocode: output fraction of (remaining items) over (items at time zero) #pseudocode: ouput remaining items as fraction or percent #pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero) #pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero) #pseudocode: outputs should be in compatible units. #pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out. #pseudocode: need test cases > small,medium, giant #pseudocode: need testcases within range of expected operation. #pseudocode: are there any cases too small or large to be solved? # # F(N+1) == F(N) + F(N-1) # F(1) == 1 # F(2) == 1 set Grade_School 6 set Middle_School 2 set High_School 4 set College 4 set Graduate_School 2 set values [list 6 8 12 16 18] set fractals [list 9.7 12.94 19.4 25.888 29.14] partials, f(1)= .5 f(2) = (1/4) * .5 f(3) = (1/6) * .5
In planning any software, it is advisable to gather a number of testcases to check the results of the program.
table 1 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
1: | testcase_number | |
11.0 : | initial age decimal years | |
17.798373876248842 : | answers: probable 2nd next occurrence, decimal years : | |
24.596747752497684 : | probable 3 next occurrence, decimal years : | |
31.395121628746526 : | probable 4 next occurrence, decimal years : | |
38.193495504995369 : | probable 5 next occurrence, decimal years : | |
44.991869381244214 : | probable 6 next occurrence, decimal years : | |
51.790243257493053 : | probable 7 next occurrence, decimal years : | |
58.588617133741892 : | probable 8 next occurrence, decimal years : |
;# printout start study of initial conditions observer value 17.792999999999999 returns prior reverse returns prior reverse 10.996678761826878 prior reverse rnd 10.997 seed event rounded 17.793 end study of initial conditions %|table 1|printed in| tcl wiki format|%
table 2 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
2: | testcase_number | |
16.0 : | initial age decimal years | |
25.888543819998318 : | answers: probable 2nd next occurrence, decimal years : | |
35.777087639996637 : | probable 3 next occurrence, decimal years : | |
45.665631459994955 : | probable 4 next occurrence, decimal years : | |
55.554175279993274 : | probable 5 next occurrence, decimal years : | |
65.442719099991592 : | probable 6 next occurrence, decimal years : | |
75.331262919989911 : | probable 7 next occurrence, decimal years : | |
85.219806739988229 : | probable 8 next occurrence, decimal years : |
;# printout start study of initial conditions observer value 16.0 returns prior reverse returns prior reverse 9.8885438199983167 prior reverse rnd 9.8885 seed event rounded 16.000 end study of initial conditions ##### start study of initial conditions observer value 25.888000000000002 returns prior reverse returns prior reverse 15.999663900757277 prior reverse rnd 16.000 seed event rounded 25.888 end study of initial conditions
table 3 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
3: | testcase_number | |
10.0 : | initial age decimal years | |
16.180339887498949 : | answers: probable 2nd next occurrence, decimal years : | |
22.360679774997898 : | probable 3 next occurrence, decimal years : | |
28.541019662496847 : | probable 4 next occurrence, decimal years : | |
34.721359549995796 : | probable 5 next occurrence, decimal years : | |
40.901699437494742 : | probable 6 next occurrence, decimal years : | |
47.082039324993694 : | probable 7 next occurrence, decimal years : | |
53.262379212492647 : | probable 8 next occurrence, decimal years : |
;# printout start study of initial conditions observer value 10.0 returns prior reverse returns prior reverse 6.1803398874989481 prior reverse rnd 6.1803 seed event rounded 10.000 end study of initial conditions start study of initial conditions observer value 16.18 returns prior reverse returns prior reverse 9.9997899379732971 prior reverse rnd 9.9998 seed event rounded 16.180 end study of initial conditions
table 3 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
3: | testcase_number | |
15.0 : | aa quantity , initial age decimal years | |
4.0 : | bb quantity | |
5.0 : | cc quantity | |
7.0 : | dd quantity | |
39.270509831248432 : | probable 2nd next occurrence, decimal years : | |
63.541019662496865 : | 3rd next occurrence, decimal years : | |
24.270509831248425 : | probable 1st next occurrence, decimal years : | |
24.271 : | probable 1st next occurrence, rounded or clipped : |
table 4 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
4: | testcase_number | |
144.0 : | entry is Fibonacci number | |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
376.98105600000002 : | successive Fibonacci number 2nd : | |
609.95534860800001 : | successive Fibonacci number 3rd : | |
232.99200000000002 : | successive Fibonacci number 1st | |
232.99 : | probable 1st next occurrence, rounded or clipped : |
If the entry is a Fibonacci number greater than zero, the TCL calculator should approximate the next 3 successive Fibonacci numbers as reals, but need to round to nearest integer. The On-Line Encyclopedia of Integer Sequences A000045 gives the Fibonacci numbers as follows 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269.
table 5 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
5: | notes on Elliott Wave Principle, possible peak curve rises and falls from Fibonacci numbers | |
wave number | entry (144) is Fibonacci number | |
wave 1 : | 161.8% | new bull (+) or bear (-) market and is usually accompanied by sentiment extremes, possible Fibonacci 161.8% plus |
wave 2 : | 61.8% | possible Fibonacci 61.8% or 78.6% retrenchment |
wave 3 : | 161.8% | possible Fibonacci 161.8% advance |
wave 4: | 38.2% | possible Fibonacci 38.2% retrenchment, sideways market |
wave 5: | 32.6% | possible Fibonacci final leg in the direction of the dominant trend |
wave 5: | 50.0% | possible Fibonacci final leg, 50.0% used as analyst midpoint and lost shirts |
Elliot wave analyst Fibonacci constants : | 161.8%.,61.8%, 38.2%, 23.6%, and 50.0 % | apparently from OEIS A000045 Fibonacci series, <3,5,8> |
The cicada insect in the USA has a life cycle of 17 years, believed to be based loosely based on the solar cycle of eleven years. Enter 10 decimal years in the TCL calculator, result rounds down to 17 years. The cicada insects emerge in May of the seventeenth year, so the hand TCL expression was expr { 17 + 5./12 } as 17.4166 or rounded 17.4 decimal years. Comment that time coincidence is not proof of causation.
Another cicada insect species in the USA has a life cycle of 13 years, possibly an unknown factor may be involved. From the Elliot wave theory, there are other Fibonacci constants for breakpoints. Skipping a number in the Fibonacci sequence (55/144 and 144/55) produces 2 more Fibonacci breakpoint constants, 38.2 percent and 261.8%. In this case the Fibonacci break constant 38.2% is of interest, so the hand TCL expression was expr { 10. * ( 1. + 100.* 38.2% ) } as expr { 10. *1.382 } to 13.819 or rounded 13.8 decimal years.
table 5a | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
5a: | testcase_number | life cycle of cicada insect |
11.0 : | aa quantity , solar cycle of eleven years | |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
28.798373876248846 : | probable 2nd next occurrence, decimal years : | |
46.596747752497691 : | 3rd next occurrence, decimal years : | |
17.798373876248846 : | probable 1st next occurrence, decimal years : | |
17.798 : | probable 1st next occurrence, rounded or clipped : | life cycle of cicada insect |
table 5b | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
5b: | testcase_number | unknown factor for separate species |
8.0 : | aa quantity , unknown factor, decimal years | |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
20.944271909999159 : | probable 2nd next occurrence, decimal years : | |
33.888543819998318 : | 3rd next occurrence, decimal years : | |
12.944271909999159 : | probable 1st next occurrence, decimal years : | |
12.944 : | probable 1st next occurrence, rounded or clipped : | life cycle of cicada insect, separate species |
Elliot wave analyst Fibonacci constants : | 161.8%.,61.8%, 38.2%, 23.6%, and 50.0 % | apparently from OEIS A000045 Fibonacci series, <3,5,8> |
breakpoint from alternate Elliot wave theory : | expr { 10. * ( 1. + 100.* 38.2% ) } 13.8 decimal years | Elliot wave theory , not proof of causation. |
;# wave analyst Fibonacci constants ;# using Fibonacci series expr 5./11 = 0.4545 ( ~ .5) expr 5./13 = 0.38461538461538464 expr 5./21 = 0.23809523809523808 expr 5./34 = 0.14705882352941177 ;# wave analyst Fibonacci constants ;# using golden ratio expr { 1/.618 } = 1.618 expr { 1/1.618 } = 0.6180469715698392 expr { .618 *.618 } = 0.381924 expr { .618 *.618 *.618 } = 0.236029032 expr { .618 *.618 *.618*.618 } = 0.14586594177599999
Most agree that humans start puberty at 13 years old and become mature at 21 years. Enter 13 years for puberty in calculator and receive rounded 21 years for human maturity.
table 6 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
6: | testcase_number | |
13.0 : | aa quantity , initial age decimal years | |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
34.034441853748632 : | probable 2nd next occurrence, decimal years : | |
55.068883707497264 : | 3rd next occurrence, decimal years : | |
21.034441853748632 : | probable 1st next occurrence, decimal years : | |
21.034 : | probable 1st next occurrence, rounded or clipped : |
Most of the golden ratio problems I can find deal with dimensions rather than time. According to Nick Braden in the book Fractal Time , one complete turn of a DNA strand is 34 angstrom units in length and 21 angstrom units wide. Enter 21 angstrom units for DNA width in TCL calculator and receive rounded 34 angstrom units for DNA height.
Perhaps an algorithm for the reverse progress would be useful, Height >> Width. The TCL expression would be expr { 34. * ( 1/ 1.618 ) } or 21.013 angstrom units width.
table 7 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
7: | testcase_number | |
21.0 : | aa quantity , width angstrom units | |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
54.978713763747791 : | probable 2nd next occurrence, decimal years : | |
88.957427527495582 : | 3rd next occurrence, decimal years : | |
33.978713763747791 : | height angstrom units : | |
33.979 : | height angstrom units : |
proc reverse_time_fractal {age_years} { set g_constant 1.61803398874989484820 set reverse_time_fractal [ expr { $age_years * (1./$g_constant) } ] ;#return $reverse_fractal }
The starfish has 5 arms and the dimensions of a pentagon in length, rather than time units. Enter 1 inch for width between two arms in TCL calculator and receive rounded 1.816 units for maximum width or length across two alternate arms. The units cancel out in the calculator, so one may enter 8 centimeters and receive proportional centimeters across 2 alternate arms, using proportional calculations with the golden mean.
table 8 | printed in | tcl wiki format |
---|---|---|
quantity | value | comment, if any |
8: | testcase_number | |
8.0 : | aa quantity , centimeters | between 2 arms |
2.0 : | bb quantity | |
3.0 : | cc quantity | |
4.0 : | dd quantity | |
20.943391999999999 : | probable 2nd next occurrence, decimal years : | |
33.886408255999996 : | 3rd next occurrence, decimal years : | |
12.943999999999999 : | probable 1st next occurrence, decimal years : | |
12.944 : | centimeters : | units cancel out, maximum starfish demensions |
Ratio of male bees to female bees in hive, 1:1.618. A single hive can have from 10,000 to well over 60,000 bees. Female should be fraction expr { 1.618/ (1.+1.618) } or 0.618.
;# pretty print from autoindent and ased editor occurrence ;# Time Fractal Proportions calculator ;# written on Windows ;# working under TCL version 8.6 ;# gold on TCL WIKI, 30apr2021 package require Tk package require math::numtheory namespace path {::tcl::mathop ::tcl::mathfunc math::numtheory } set tcl_precision 17 frame .frame -relief flat -bg aquamarine4 pack .frame -side top -fill y -anchor center set names {{} {initial age decimal years :} } lappend names {answers: probable 2nd next occurrence, decimal years : } lappend names {probable 3 next occurrence, decimal years : } lappend names {probable 4 next occurrence, decimal years : } lappend names {probable 5 next occurrence, decimal years : } lappend names {probable 6 next occurrence, decimal years : } lappend names {probable 7 next occurrence, decimal years : } lappend names {probable 8 next occurrence, decimal years : } foreach i {1 2 3 4 5 6 7 8} { label .frame.label$i -text [lindex $names $i] -anchor e entry .frame.entry$i -width 35 -textvariable side$i grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 } proc about {} { set msg "Calculator for Time Fractal Proportions V2 from TCL WIKI, written on TCL 8.6 " tk_messageBox -title "About" -message $msg } proc self_help {} { set msg "Calculator for Time Fractal Proportions V2 from TCL , ;# self help listing ;# 1 given follow. 1) initial age decimal years N1 ;# This calculator uses golden ratio proportions ;# to predict successive time windows or time fractals ;# of similar probable occurrences based ;# a seed time or initial age decimal years. ;# There is plenty of uncertainty about probable occurrences ;# and events after the seed time, but the ;# the probable occurrences are largely based on growth, ;# accumulation, and succession ;# following the golden ratio proportions. ;# Not all events in time have golden ratio proportions. ;# For comparison, TCL code may include redundant paths & formulas. ;# The TCL calculator normally uses modern ;# units for convenience to modern users and textbooks. ;# Any convenient and consistent in/output units might be used ;# like inches, feet, nindas, cubits, or dollars to donuts. ;# Recommended procedure is push testcase and fill frame, ;# change first three entries etc, push solve, ;# and then push report. Report allows copy and paste ;# from console to conventional texteditor. For testcases ;# testcase number is internal to the calculator and ;# will not be printed until the report button is pushed ;# for the current result numbers. ;# This posting, screenshots, and TCL source code is ;# copyrighted under the TCL/TK 8.6 license terms. ;# Editorial rights retained under the TCL/TK license terms ;# and will be defended as necessary in court. Conventional text editor formulas or grabbed from internet screens can be pasted into green console. Try copy and paste following into green screen console set answer \[* 1. 2. 3. 4. 5. \] returns 120 ;# gold on TCL Club, 30apr2021 " tk_messageBox -title "self_help" -message $msg } proc precisionx {precision float} { ;# tcl:wiki:Floating-point formatting, <AM> ;# select numbers only, not used on every number. set x [ expr {round( 10 ** $precision * $float) / (10.0 ** $precision)} ] ;# rounded or clipped to nearest 5ird significant figure set x [ format "%#.5g" $x ] return $x } proc time_fractal {age_years} { set g_constant .6180339887498948420 ;# golden ratio is 1.6180339887498948420 set year_occurrence [ expr { $age_years + $g_constant * $age_years } ] return $year_occurrence } proc reverse_time_fractal {age_years} { set g_constant 1.61803398874989484820 set reverse_time_fractal [ expr { $age_years * (1./$g_constant) } ] ;#return $reverse_fractal } proc calculate { } { global answer2 global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number incr testcase_number set side1 [* $side1 1. ] set side2 [* $side2 1. ] set side3 [* $side3 1. ] set side4 [* $side4 1. ] set age_years [ expr { $side1*1.0 } ] ;# golden conjugate is 0.61803398874989484820 ;# alternate test value for ;# golden conjugate is 0.618 ;# but do not see much difference on small numbers ;# under 20 set g_constant 0.61803398874989484820 set year_occurrence [ time_fractal $age_years ] set side2 $year_occurrence ;# start study of initial conditions on seed event puts "start study of initial conditions " ;# reverse operation is of interest in ;# observer problem finding seed event value if unknown puts "observer value $age_years returns prior reverse" puts "returns prior reverse [reverse_time_fractal $age_years] " puts "prior reverse rnd [ precisionx 6 [reverse_time_fractal $age_years]] " puts " seed event rounded [precisionx 5 $age_years ] " puts "end study of initial conditions " set time_cycle [ expr { $year_occurrence - $age_years } ] set side3 [ expr { $age_years + $time_cycle + $time_cycle } ] set side4 [ expr { $age_years + 3 * $time_cycle } ] set side5 [ expr { $age_years + 4 * $time_cycle } ] set side6 [ expr { $age_years + 5 * $time_cycle } ] set side7 [ expr { $age_years + 6 * $time_cycle } ] set side8 [ expr { $age_years + 7 * $time_cycle } ] } proc fillup {aa bb cc dd ee ff gg hh} { .frame.entry1 insert 0 "$aa" .frame.entry2 insert 0 "$bb" .frame.entry3 insert 0 "$cc" .frame.entry4 insert 0 "$dd" .frame.entry5 insert 0 "$ee" .frame.entry6 insert 0 "$ff" .frame.entry7 insert 0 "$gg" .frame.entry8 insert 0 "$hh" } proc clearx {} { foreach i {1 2 3 4 5 6 7 8 } { .frame.entry$i delete 0 end } } proc reportx {} { global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number console show; puts "%|table $testcase_number|printed in| tcl wiki format|% " puts "&| quantity| value| comment, if any|& " puts "&| $testcase_number:|testcase_number | |&" puts "&| $side1 :|initial age decimal years | |&" puts "&| $side2 :|answers: probable 2nd next occurrence, decimal years : | |& " puts "&| $side3 :|probable 3 next occurrence, decimal years : | |& " puts "&| $side4 :|probable 4 next occurrence, decimal years : | |&" puts "&| $side5 :|probable 5 next occurrence, decimal years : | |&" puts "&| $side6 :|probable 6 next occurrence, decimal years : | |&" puts "&| $side7 :|probable 7 next occurrence, decimal years : | |&" puts "&| $side8 :|probable 8 next occurrence, decimal years : | |&" } frame .buttons -bg aquamarine4 ::ttk::button .calculator -text "Solve" -command { calculate } ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 11. 17.79 24.59 31.39 38.19 44.99 51.79 58.58} ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 10.0 16.18 22.36 28.54 34.72 42.360 47.08 53.26 } ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 15.0 24.27 33.54 42.81 52.08 61.35 70.62 79.89 } ::ttk::button .clearallx -text clear -command {clearx } ::ttk::button .about -text about -command {about} ::ttk::button .self_help -text self_help -command {self_help } ::ttk::button .cons -text report -command { reportx } ::ttk::button .exit -text exit -command {exit} pack .calculator -in .buttons -side top -padx 10 -pady 5 pack .clearallx .cons .self_help .about .exit .test4 .test3 .test2 -side bottom -in .buttons grid .frame .buttons -sticky ns -pady {0 10} . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30 wm title . "Time Fractal Proportions Calculator V2 "
For the push buttons, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. For testcases in a computer session, the TCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared either on the next clear button or on the next solve button.
Please place any comments here, Thanks, gold 30Apr2021
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