Time Fractals in Golden Ratio Proportions and TCL demo example calculator, numerical analysis

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


Introduction


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.


Body


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.


Conclusions


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, Equations, and Wiki Page Checklist

     #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?

Testcases Section

In planning any software, it is advisable to gather a number of testcases to check the results of the program.

Testcase 1

table 1printed in tcl wiki format
quantity value comment, if any
1:testcase_number
11.0 :aa quantity , initial age decimal 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 :

Testcase 2


table 2printed in tcl wiki format
quantity value comment, if any
2:testcase_number
10.0 :aa quantity , initial age decimal years
5.0 :bb quantity
7.0 :cc quantity
9.0 :dd quantity
26.180339887498953 :probable 2nd next occurrence, decimal years :
42.360679774997905 :3rd next occurrence, decimal years :
16.180339887498949 :probable 1st next occurrence, decimal years :
16.180 :probable 1st next occurrence, rounded or clipped :

Testcase 3


table 3printed 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 :

Testcase 4


table 4printed 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 5printed 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>

Testcase 5


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 5aprinted 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

Testcase 6


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 6printed 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 :


Testcase 7


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 7printed 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 year_occurrence  [ expr {  $age_years * (1./$g_constant)   } ]
            return $year_occurrence
            }


Testcase 8



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 8printed 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


Testcase 9


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.


Screenshots Section


figure 1.


time_fractals_equation



figure 2.


time_fractal_dummy_curve



figure 3.


Time_Fractal_starfish


figure 4.


Golden_Ratio_Proportions


References:

  • Wikipedia search engine < time >
  • Wikipedia search engine < golden ratio proportions >
  • Wikipedia search engine < Fibonacci >
  • Google search engine < fractal time calculator Braden Greg >
  • Book >> Fractal Time: The Secret of 2012 and a New World Age
  • Paperback – Illustrated, February 1, 2010
  • book(s) by Braden Gregg
  • www.greggbraden.com/fractal time calculator
  • Website articles by Tony Spilotro
  • Bitcoin Mathematics: Why 21 Million BTC May Have Been Chosen
  • Extreme interest in trading Bitcoin cryptocurrency golden ratio tops
  • Fibonacci Day: How To Use Math To Trade Bitcoin And Altcoins
  • Web article Mathematical Mystery: Why Did The Bitcoin Rally Stop At The Golden Ratio?
  • Crypto Calculated: How Ancient Math Predicts Bitcoin’s Next Top At $270K
  • Fibonacci Day: How To Use Math To Trade Bitcoin And Altcoins
  • by Tony Spilotro
  • Understanding Bitcoin’s Market Cycles: 3 Simple indicators for future tops and bottoms
  • Collected Works of R. N. Elliot
  • The Wave Principle. Nature's Law: The Secret of the Universe. R. N. Elliot
  • Series of Articles Published in 1939 by Ralph Nelson Elliott.
  • Elliott Wave Principle by A.J. Frost and Robert Prechter
  • Elliott Wave Principle: Key To Market Behavior
  • Elliott, Ralph Nelson, Frost, Alfred John, Prechter, Robert Rougelot
  • R.N. Elliott's Masterworks: The Definitive Collection
  • 318 Pages · 1994 English
  • by R. N. Elliott & Robert R. Prechter & Jr.
  • Fractal Time. coded in python , sourceforge.net_projects_fractaltimecalc
  • Golden Ratios in Energy Radiation and Vibrations
  • May 23, 2012 by Gary Meisner 1.6180339887498948420
  • Terence McKenna. 1998, TimeWave Zero Software
  • Essay: Timewave Zero .Pdf by Terence McKenna
  • contributions on Time Code Software by Peter Meyer.
  • Peter J. Meyer , Peter Johann Gustav Meyer, born 1946
  • Mathematics of Timewave Zero by Peter Meyer.
  • appeared in the Invisible Landscape, 2nd edition, HarperCollins, 1993
  • www.science20.com/hammock_physicist/fibonacci_butterflies
  • by Johannes Koelman, August 6th 2009
  • en.wikipedia.org/wiki/Anosov_diffeomorphism, Dmitri Victorovich Anosov
  • Fractal universe and the speed of light: Revision of the universal constants
  • Antonio Alfonso-Faus


Appendix Code

appendix TCL programs and scripts

        ;# 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 {{} {aa quantity, initial age decimal years  :} }
        lappend names {bb quantity optional :}
        lappend names {cc quantity optional : }
        lappend names {dd quantity optional : }
        lappend names {answers: probable 2nd next occurrence, decimal years  :}
        lappend names {probable 3rd next occurrence, decimal years  : }
        lappend names {probable  1st next occurrence, decimal years  : }
        lappend names {probable  1st next occurrence, rounded or clipped  :} 
        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
            ;# 4 givens follow.
            1) aa initial age decimal years  N1
            2) bb  optional N2
            3) cc  optional N3
            4) dd  optional N4
            ;# 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
            ;# 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 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 2nd_occurrence  [    time_fractal $year_occurrence   ]  
            set side5  $2nd_occurrence
            set 3rd_occurrence [    time_fractal $2nd_occurrence  ] 
            set side6  $3rd_occurrence
            set side7  $year_occurrence
            set side8 [precisionx 5  $year_occurrence ]
             }
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$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 :|aa quantity , initial age decimal years  |   |&"
            puts "&| $side2 :|bb quantity   | |& "  
            puts "&| $side3 :|cc quantity   | |& "
            puts "&| $side4 :|dd quantity   | |&"
            puts "&| $side5 :|probable 2nd next occurrence, decimal years  : | |&"
            puts "&| $side6 :|3rd next occurrence, decimal years : |  |&"
            puts "&| $side7 :|probable  1st next occurrence, decimal years : |  |&"
            puts "&| $side8 :|probable  1st next occurrence, rounded or clipped : |  |&" 
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 11. 2.  3.0 4.  28.798  46.596  17.79837 17.798}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 10.0 5.0 7.0 9.0  26.180  42.360  16.18033 16.180 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 15.0 4.  5.0 7.0   39.270  63.541  24.27050 24.271 }
        ::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 "           

Pushbutton Operation

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.


Comments Section

Please place any comments here, Thanks, gold 30Apr2021