**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 ---- <<TOC>> *** Introduction*** ----[gold] Here are some calculations on time fractal windows. This calculator uses golden ratio proportions to predict successive time windows or successive time fractals of similar probable occurrences based either a seed time or initial age in 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. ---- *** Golden Ratio Constants *** ---- 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 Elliot wave analyst Fibonacci constants : 161.8%.,61.8%, 38.2%, 23.6%, and 50.0 % are apparently derived from OEIS A000045 Fibonacci series, <3,5,8>. An Elliot wave is defined as two strokes, up and down. For example, an Elliot wave might have a rise (factor) of 0.618 and a fall (factor) of 0.382, where the initial position point or reference point is scaled and normalized to unity (1). If the calculator entry is a Fibonacci number greater than zero, the TCL calculator should approximate the next 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. ---- *** Test Suite on Time Fractals in Golden Ratio Proportions *** ---- The calculations of time fractals in golden ratio proportions have problems with initial conditions and observer reference issues. There are two possible methods of time fractal calculations, either the seed year as personal age or the seed year as a Gregorian calendar year. The seed age event and birthdays are different for most people in the personal age method. The optional test suite has added the calculations for a golden date from a Gregorian calendar year. ---- *** 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 percent accuracy. ---- *** 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? # # 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 ====== ---- ***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 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|% ====== ---- **** Testcase 2 **** ---- ---- %|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 ====== ---- **** Testcase 3 **** ---- ---- ---- %|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 ====== ---- **** Testcase 4 **** ---- %|table 8|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 8:|testcase_number | |& &| 15.0 :|initial age decimal years | |& &| 24.270509831248422 :|answers: probable 2nd next occurrence, decimal years : | |& &| 33.541019662496844 :|probable 3 next occurrence, decimal years : | |& &| 42.811529493745269 :|probable 4 next occurrence, decimal years : | |& &| 52.082039324993687 :|probable 5 next occurrence, decimal years : | |& &| 61.352549156242105 :|probable 6 next occurrence, decimal years : | |& &| 70.623058987490538 :|probable 7 next occurrence, decimal years : | |& &| 79.893568818738956 :|probable 8 next occurrence, decimal years : | |& ---- ====== ;# printout start study of initial conditions observer value 15.0 returns prior reverse returns prior reverse 9.2705098312484218 prior reverse rnd 9.2705 seed event rounded 15.000 end study of initial conditions start study of initial conditions observer value 24.27 returns prior reverse returns prior reverse 14.999684906959946 prior reverse rnd 15.000 seed event rounded 24.270 end study of initial conditions ====== ---- ---- **** Testcase 5, successive Fibonacci numbers **** ---- %|table 10|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 10:|testcase_number | |& &| 144.0 :|initial age decimal years | |& &| 232.99689437998484 :|answers: probable 2nd next occurrence, decimal years : | |& &| 321.99378875996968 :|probable 3 next occurrence, decimal years : | |& &| 410.99068313995451 :|probable 4 next occurrence, decimal years : | |& &| 499.98757751993935 :|probable 5 next occurrence, decimal years : | |& &| 588.98447189992419 :|probable 6 next occurrence, decimal years : | |& &| 677.98136627990903 :|probable 7 next occurrence, decimal years : | |& &| 766.97826065989386 :|probable 8 next occurrence, decimal years : | |& ---- ====== ;# printout start study of initial conditions observer value 144.0 returns prior reverse returns prior reverse 88.996894379984852 prior reverse rnd 88.997 seed event rounded 144.00 end study of initial conditions start study of initial conditions observer value 232.99600000000001 returns prior reverse returns prior reverse 143.99944724277049 prior reverse rnd 144.00 seed event rounded 233.00 end study of initial conditions ====== ---- ---- If the entry is a Fibonacci number greater than zero, the TCL calculator should approximate the next 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>|& ---- **** Testcase 6, life cycle of cicada insect and separate cicada species**** ---- 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. In this problem, we used reverse logic or the reverse golden ratio proc. What number of years would return a life cycle of 13 years? So the hand TCL expression was expr { $age_years * (1./1.618) } as or rounded 8 decimal years. ---- ====== ,# printout start study of initial conditions observer value 13.0 returns prior reverse returns prior reverse 8.034441853748632 prior reverse rnd 8.0344 seed event rounded 13.000 ====== ---- %|table 6a |printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 6a :|testcase_number | |& &| 11.0 :|initial age decimal years | solar cycle of eleven years |& &| 17.798373876248842 :|answers: probable 2nd next occurrence, decimal years. life cycle of cicada insect : | |& &| 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 11.0 returns prior reverse returns prior reverse 6.798373876248843 prior reverse rnd 6.7984 seed event rounded 11.000 end study of initial conditions start study of initial conditions observer value 17.0 returns prior reverse returns prior reverse 10.506577808748212 prior reverse rnd 10.507 seed event rounded 17.000 end study of initial conditions %|table 14|printed in| tcl wiki format|% ====== ---- %|table 6b|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 6b:|testcase_number | |& &| 8.0 :|initial age decimal years |unknown factor for separate species |& &| 12.944271909999159 :|answers: life cycle of cicada insect species, decimal years : | |& &| 17.888543819998318 :|probable 3 next occurrence, decimal years : | |& &| 22.832815729997478 :|probable 4 next occurrence, decimal years : | |& &| 27.777087639996637 :|probable 5 next occurrence, decimal years : | |& &| 32.721359549995796 :|probable 6 next occurrence, decimal years : | |& &| 37.665631459994955 :|probable 7 next occurrence, decimal years : | |& &| 42.609903369994115 :|probable 8 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. |& ---- ====== ;# printout start study of initial conditions observer value 8.0 returns prior reverse returns prior reverse 4.9442719099991583 prior reverse rnd 4.9443 seed event rounded 8.0000 end study of initial conditions start study of initial conditions observer value 13.0 returns prior reverse returns prior reverse 8.034441853748632 prior reverse rnd 8.0344 seed event rounded 13.000 end study of initial conditions %|table 16|printed in| tcl wiki format|% ====== ====== ;# 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 ====== ---- From 24 October 1929 to 29 October 1929, the American stock market lost 23 per cent of value. Possibly the Elliot wave analyst Fibonacci constant of 0.236029032 or 23.6% may apply. ---- **** Testcase 7 **** ---- 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 17|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 17:|testcase_number | |& &| 13.0 :|initial age decimal years | |& &| 21.034441853748632 :|answers: probable 2nd next occurrence, decimal years : | |& &| 29.068883707497264 :|probable 3 next occurrence, decimal years : | |& &| 37.103325561245896 :|probable 4 next occurrence, decimal years : | |& &| 45.137767414994528 :|probable 5 next occurrence, decimal years : | |& &| 53.17220926874316 :|probable 6 next occurrence, decimal years : | |& &| 61.206651122491792 :|probable 7 next occurrence, decimal years : | |& &| 69.241092976240424 :|probable 8 next occurrence, decimal years : | |& ---- ====== #; start study of initial conditions observer value 13.0 returns prior reverse returns prior reverse 8.034441853748632 prior reverse rnd 8.0344 seed event rounded 13.000 end study of initial conditions ====== ---- **** Testcase 8 **** ---- 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 18|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 18:|testcase_number | |& &| 21.0 :|angstroms width | |& &| 33.978713763747791 :|answers: probable 2nd next occurrence, angstroms : | |& &| 46.957427527495582 :|probable 3 next occurrence, decimal years : | |& &| 59.936141291243374 :|probable 4 next occurrence, decimal years : | |& &| 72.914855054991165 :|probable 5 next occurrence, decimal years : | |& &| 85.893568818738956 :|probable 6 next occurrence, decimal years : | |& &| 98.872282582486747 :|probable 7 next occurrence, decimal years : | |& &| 111.85099634623454 :|probable 8 next occurrence, decimal years : | |& ---- ====== start study of initial conditions observer value 21.0 returns prior reverse returns prior reverse 12.978713763747791 prior reverse rnd 12.979 seed event rounded 21.000 end study of initial conditions ====== ---- ---- ---- ---- ---- ====== proc reverse_time_fractal {age_years} { set g_constant 1.61803398874989484820 set reverse_time_fractal [ expr { $age_years * (1./$g_constant) } ] ;#return $reverse_fractal } ====== ---- ---- **** Testcase 10 **** ---- ---- 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 12.9 centimeters across 2 opposing arms, using proportional calculations with the golden mean. ---- %|table 2|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 2:|testcase_number | |& &| 8.0 :|centimeters between 2 adjacent arms | |& &| 12.944271909999159 :|answers: maximum starfish dimensions across 2 opposing arms : | |& &| 17.888543819998318 :|probable 3 next occurrence, decimal years : | |& &| 22.832815729997478 :|probable 4 next occurrence, decimal years : | |& &| 27.777087639996637 :|probable 5 next occurrence, decimal years : | |& &| 32.721359549995796 :|probable 6 next occurrence, decimal years : | |& &| 37.665631459994955 :|probable 7 next occurrence, decimal years : | |& &| 42.609903369994115 :|probable 8 next occurrence, decimal years : | |& ---- ---- **** Testcase 11 **** ---- 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. Enter 10000 males for a beehive and TCL calculator estimates 16180 females in hive. ---- %|table 3|printed in| tcl wiki format|% &| quantity| value| comment, if any|& &| 3:|testcase_number | |& &| 10000.0 :|number of male bees | |& &| 16180.339887498947 :|answers: number of female bees : | |& &| 22360.679774997894 :|probable 3 next occurrence, decimal years : | |& &| 28541.019662496841 :|probable 4 next occurrence, decimal years : | |& &| 34721.359549995788 :|probable 5 next occurrence, decimal years : | |& &| 40901.699437494739 :|probable 6 next occurrence, decimal years : | |& &| 47082.039324993682 :|probable 7 next occurrence, decimal years : | |& &| 53262.379212492626 :|probable 8 next occurrence, decimal years : | |& ---- ***Screenshots Section*** ---- ****figure 1.Golden_Ratio_screenshot**** ---- [Golden_Ratio_screenshot] ---- ****figure 2.time_fractals_equation**** ---- [time_fractals_equation] ---- ---- ****figure 3.time_fractal_dummy_curve**** ---- [time_fractal_dummy_curve] ---- ---- ****figure 4. Time_Fractal_Starfish**** ---- [Time_Fractal_starfish] ---- ****figure 5.Golden_Ratio_Proportions**** ---- [Golden_Ratio_Proportions] ---- ****figure 6.Golden_Ratio_definition**** ---- [Golden_Ratio_definition] ---- ****figure 7.Golden_Ratio_waves**** ---- [Golden_Ratio_more_waves] ---- ***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 * Weinberg, S. (1972) Gravitation and Cosmology. Wiley, * Timewave Synthesizer at SourceForge * waveform synthesizer based upon Timewave Zero theory by Terence McKenna ---- ---- **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 {{} {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 calendar_year_golden { gregorian_date } { global side1 side2 side3 side4 side5 global side6 side7 side8 global testcase_number set golden_ratio 1.6180339887498948420 set golden_c .6180339887498948420 ;# initial test number set gregorian_date 1941.12 ;# gregorian_date 1941.12 returns golden date 1984.32 set conversion_date 3113. set absolute_date [ expr { $gregorian_date + $conversion_date}] set lapsed_portion_cycle [ expr { $absolute_date / 5125.} ] set phi_x_lapsed_portion [ expr { $lapsed_portion_cycle * $golden_c} ] set cycle_balance [ expr { 5125. - $absolute_date} ] set interval_fm_seed_year [ expr { $cycle_balance * $phi_x_lapsed_portion} ] set next_date [ expr { $absolute_date + $interval_fm_seed_year} ] set next_date_gregorian [ expr { $next_date - 3113.} ] ;# returns answer in decimal years return $next_date_gregorian } proc initial_conditions_check {age_years } { global side1 side2 side3 side4 side5 global side6 side7 side8 ;# test suite follows ;# start study of initial conditions on seed event ;# test suite for Time Fractal Proportions calculator puts " test suite for Time Fractal Proportions calculator " puts " start study of initial conditions " #; checking calendar year proc puts " initial test number set gregorian_date 1941.12 " puts " gregorian_date 1941.12 returns golden date 1984.32 " puts " gregorian 1941.12 returns golden date [ calendar_year_golden 1941.12 ] " puts " testing age_years from first entry loaded as gregorian year $age_years" puts " gregorian $age_years returns golden date [ calendar_year_golden $age_years ] " ;# 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 " } 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 } ] ;# block following to omit initial_conditions test suite set seed_year [ initial_conditions_check $age_years ] ;# 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 set initial_year [ ] 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 " ====== ---- *** 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** <<discussion>> Please place any comments here, Thanks, [gold] 30Apr2021 <<categories>> Numerical Analysis | Toys | Calculator | Mathematics| Example| Toys and Games | Games | Application | GUI ---- <<categories>> Development | Concept| Algorithm