It really isn't an easy subject when it comes to doing and omnifferencings twixt classical and quantum are immense.

We have tools to do classical fractals. We lack a huge number of quantum~tools including understanding to do quantum~fractals.

Classical Fractals and Quantonic/Quantum Fractals- See our c.e. 2008 Classical vis-à-vis Quantum Fractals re: Cantor dust.

Classical Fractals:Benoit Mandelbrot - Father of Classical Fractal Meme

- See Mandelbrot's
Fractal Geometry of NatureClassical Definition of 'Fractal,' — Classical Fractals

:

- are objective — See our SOM Philosophy reality table (based upon Aristotelian ideal, concepts about 'matter/substance')

- quantitative
- formal predicate unilogical
- are dichonic
- are state-ic

- are radically formal (radically mechanistic; adhere classically mathematical mechanics)
- are radically final (suffer classically conditional haltability/stoppability)
- assume fractal objects are lisr

- i.e., they assume an Aristotelian objective excluded-middle based upon Aristotle's syllogistic 'laws
:'

A classically 'equals' A

('law' of identity) A must be

eitherAornot A('law' of contradiction)

Polemicizes a classicaleither/ordichonic EOOO reality. See Henri Louis Bergson's cogent remarks on classical 'contradiction.' See in particular his, "...we shall never affirm a thing is not."A cannot be

bothAandnot A('law' of excluded-middle)

Denies quantum reality's quantonic BAAM coherence/compenetration/coinsidence.

Note: Dear reader, if you are new to Quantonics, it is important for you to know that Aristotle's syllogistic 'laws'bothdenyandoutlawquantum reality. In Quantonics we deny Aristotle's syllogistic 'laws.' If you spend some times with them you may arrive at our conclusion:Aristotle's syllogistic 'laws' are silly. See our Aristotle Connection.

- etc.
Classical Fractal Examples

:Classical Fractals as Classical Sophisms

Classical sophisms are self-referent and classically recursive. As we know from our other work regarding Buridan's Sophismata, then, classical fractals must be classical sophisms. Why? They are, when chaotic, classically inconsistent! Buridan and Hughes classically agree that all contextually inconsistent propositions are FALSE! Also, we know that classical fractals often manufacture many (often self-similar) incommensurable islands of many truths. To Buridan and Hughes these are sophisms and innately FALSE!

Saying sophisms "are FALSE" is equi-valent (analogous to) saying "quantum reality is FALSE!"

Classical Fractals as Manufacturers of Many Polylogical Truths (CR's "Chaos.")

Classical Non-generative Processes

Any notions of real quantum~evolution are entirely absent in classical mechanics

Classical Generative/Manufacturing Processes

Classical Call-entrancy

Classical Re-entrancy

Classical Self-reference

Classical Recursion

Clocked Classical Recursion

Unclocked (Self) Classical Recursion (requires dedicated classical unit processors per sophism to emulate Planck rate quantum~monitoring essence; that's pretty much why any classical approach torealquantum computing shall fail; we can classically, n¤n real time scheduler-emulate, however; how would we use this? see our fuzzons to fermion onta — we could use this approach to do endergonic exergonic switching; Doug - 15Sep2005)A Classical Equal Meme - There is

Classical 'Equal' (See discussion and our comments under Incommensurability as Contrafactual Definiteness.)no

So, in general, exactly how do we

dofractals classically?In terms of classical mathematics it looks like this

:x _{n+1}= f(x_{n}) - Simply, calculate next formally using prior...That is called a "one 'di'mensional recurrence relation." It may be generalized to N 'di'mensions. If you want a

realclassical exemplar search for fractals on www. Also see Doug Hofstadter'sMetamagical Themas.Every parcel of that 'equation' is ideally mechanical. Purpose of said assumed predicable analytical mechanicity is ideal formality of mathematics and its functions. Its results are always absolute

:bothconsistent formally and complete formally.Said index 'n' is always an integer. Said 'variable' 'x' is always 'rational,' and never probabilistic, plausibilistic, nor likelihoodistic. 'n' and 'x' never change (always retain monistic 'state') until changed, and only monistically changed under

controlled classicalconditions. Ditto 't.' Classical time too, is monistic:OSFA.Said 'x' is axiomatically independent; 'n' too. They neither effect nor affect any other 'variable(s)' mechanically unattached (compare to Polanyi's "mathematics as middle-inclusion;" this is one of his most remarkable insights...) to it in said or other formal equation. Significates which obey these classical rules are called

objectsandobjective. Real objects are always monistically y=f(t)continuous in monistic classical 'state,' until monistically changed by a classical 'event.' Doug uses dichon(~, o) to illustrate this classical, dialecticalcontinuous functional orthodoxy:Classical theory, be it Einsteinian-Newtonian, be it quantum~mechanical is

continuous in nature, predicable macroscopically, and never stochastic. Quantum-mechanically our waveform iscontinuous andalways a Fourier algebraic synthesis of pure dialectical plus-minus alternating sinusoids. So y=f(t) is a dialectical waveform's general description classically.We emphasize here

:classicists do not view waves depicted above as all quantumly~positive probability, nor do they view them as syntheses of discrete positive probabilities or ensembles of positive stochastics. They view waves as classically plus-minus alternating, predicable, predictable, mechanically deterministic, and absolutely and nonsceptically certain:We see one of many notable classical failures of thought. Ours, i.e., Quantonics', is a major distinction required for thought and then understanding how classical theory is so vastly different (invalidly inferior) from quantum theory and even more different from real Bohmian non mechanical quantum empiritheory. To a classicist y=f(t) is a rational dialectical orthodox fact. Now recall Hume's Law:"There is no bridge over fact and value." That is SOM's wall! It defines classical thinking methods (CTMs) innately. A classical exemplar may be perused at EPR.Classical theory whether Newtonian whether quantum-mechanical claims there are two views of reality: either particle (o) or wave (~). Particles are objects and waves are y=f(t) objective. No classical object can change,

per se. Again, ours is a major distinction:objective fact vav subjective Value. All subjective Value is simply denied classically ascontrafactual 'value.' Thus said wall. AKA Hume's Law.For any given classical fractal, you may compute it state-continuous-stoppably objectively and graph it state-

continuous-stoppably objectively on a formal computer and it will alwaysappear same(repetitively identical), as long as y=f(t) equation does not mechanically change, is not mechanically changed. So for any given fractal equation we may say that we have a formal monism for that fractal:a single (one) equation which will monistically reproduce that fractal at ourDemos will. No classical fractal, no ideal objective fractal can change,per se. If you think it could, explain how, in an ideally classical, dialectical, objective worldthatis possible. (Consider self-modifying code, fractal code...HPcircalate 1960s early 1970s built computers which supported self modifying code as 'features.' (Said feature was a cheap single 'register' NOP entry point 'stack.') But that code wouldn't run in ROM, so HP altered their architectures to eliminate said 'feature.' Doug, prior GPS, worked on polar-orbit SATNAV systems using doppler slant range change (fractals) to calculate position information. GPS today has moved hugely toward more subjective stochastic methods for precise loci determination. In futures nav technologies will move radically closer to quantum, non classical renditions. Quintessentially good stochastics themselvesarefractal. Evolution itself is fractal: quantum~fractal.)For now, though, classical mathematics, like all else, must be a slave to its master

:humankind'sDemos will.Doug - 12Apr2010.

Quantonics - Parent ¤f Quantum Fractal Meme

Quantonics/Quantum Omniscrihpti¤n ¤f 'Frahctal' — Quantum Fractals

:

- are quantonic — See ¤ur MoQ Phil¤s¤phy reality table (basæd uhpon quantum comcæpts ab¤ut latched (fermi¤nihc, b¤s¤nihc, et al.) amd umlatched (is¤tr¤pic, is¤nic, et al.) quantum flux). See our Quanton Primer.
- as quantonic are thus
:

- qualitative
- quantum paral¤gical
- are phase-ic (quanton's are animate amd may c¤¤bsfect ¤næ an¤thær's quantal phases
b¤thl¤cahllyamdn¤nl¤cahlly — sææ ¤ur Planck quanton b¤th animate and inanimate semi¤tics). Ahll¤w uhs an ¤pp¤rtuhnihty hæræ t¤ uhsæ ¤ur ræcænt BAAM acronym as a quanton t¤ e[tændings ¤ur "b¤thl¤cahllyamdn¤nl¤cahlly" t¤ BAAM(l¤cally,n¤nl¤cally), which interpreted using QTMs gives, "b¤th-all n¤nl¤cally amd-many l¤cally." And even better, we may extend fr¤mb¤thl¤calityamdn¤nl¤cality t¤b¤thlisramdn¤nlisr in a similar way:BAAM(n¤nlisr,lisr). Latter is alm¤st a full Quantonic anal¤gue ¤f quantum reality. Use ¤f an even m¤re recent acr¤nym, BAWAM, m¤ves us cl¤ser t¤ abetter,animateanal¤gue ¤f quantum reality.- as phase-ic are thus
:

- radically phase-ensehmble-st¤chastic (radically quantum n¤n-mechanistic; adhere Quantonics; see David Bohm's c¤mments ¤n quantum n¤n-mechanics)
- radically unst¤ppable (quantum flux c¤mpels abs¤lutæ changæ)
- assume quantonic fractals are BAWAM(n¤nlisr,lisr)

- i.e., they assumæ a sihnglæ quantum prægmal¤gihcal ihncludæd-mihddle s¤phism
:where A issi a quanton.

A issi BAWAM n¤t A

N¤te: Dæar ræhdær, ihf y¤u aræ n¤vel t¤ Quantonics, iht issi ihmp¤hrtant f¤r y¤u t¤ kn¤w that Arihst¤tle's syllogistihc 'laws' b¤th bælihæ amd ¤utlaw quantum ræhlihty. Ihn Quantonics wæ bælihæ Arihst¤tle's syllogistihc 'laws.' Sææ ¤ur Aristotle Connection.- etc.

Quantonics/Quantum Fractal Examples

:Quantum Fractals as Sophisms

Quantonics/Quantum Fractals as Emerscenture of Many Paralogical Truths (CR's "Chaos.")

Quantonics/Quantum Emergent Processes

Quantonics/Quantum Self-reference

Quantonics/Quantum Ræcursi¤n

:

Synchr¤n¤uhs Plahnck Ratæ Quantum Ræcursi¤n Asynchr¤n¤uhs Plahnck Ratæ Quantum Ræcursi¤n Quatr¤t¤m¤uhs

Quantum C¤heræncy

— Is¤c¤herænt Plahnck Ratæ Quantum Ræcursi¤n— C¤herænt Plahnck Ratæ Quantum Ræcursi¤n — Dæc¤herænt Plahnck Ratæ Quantum Ræcursi¤n — Mihxc¤herænt Plahnck Ratæ Quantum Ræcursi¤n

Quatr¤t¤m¤uhs

Quantum Æntr¤py

— Nægæntr¤pihc Plahnck Ratæ Quantum Ræcursi¤n— Zær¤æntr¤pihc Plahnck Ratæ Quantum Ræcursi¤n — P¤sæntr¤pihc Plahnck Ratæ Quantum Ræcursi¤n — Mihxæntr¤pihc Plahnck Ratæ Quantum Ræcursi¤n A Quantonics/Quantum Equal Meme

Fractal Nature - Fractal Reality - How?

So, in general, exactly how do we

dofractals quantumly?Nature already does it. Arteries and veins in your body are ~infinitely long fractal networks. Tree limbs and branches and leaf variegations. Chambers in a nautilus. Coast lines. Mountains. Too, nature's ensemble~fractal quantum~evolutionary~modalityings manifest in classical numbers

:123. 1.618... m=1+1/m. Mantissa plus one equals one plus one/(one plus mantissa). Mantissa plus one equals one plus its reciprocal.Positive square root of five is 1.618... plus 0.618...Philosophically they manifest too as quantum~enthymemetic~memeos of Golden rectangle. The 'god number.' Phi. Philo.Five.Sophia.Magdalene. Fibonacci additive~primes, not all of which are multiplicative primes. Delta-modulation. Etc. Neat, eh? Doug - 13-14Apr2010So in terms of Quantonics' quantum~heuristics it may look somewhat like this

:What Doug's now three-plus year old graphic shows is a fractal that you want to

doin center of five other quantum~fractal ensemble~attractors all of which are evolving and responsibly coobsfecting that fractal ensemble which you are about todo.

Adaptation and De(omni)cision Making:We call them, "Ensemble holographic omnimensional quantum~self~other recurrencings network interrelationshipings."

You may look at your ensemble as a new (n¤væl) energy~welling in our local universe's ensemble of attractors as relevant and responsible energy wellings which coobsfect in heterogeneous timings and affectings (we may say, "plural ephemera" interrelatings) what you are about to

do. Crucial to be k~now~ings at this juncture is how quantum~responsibility requiresalltoadaptto what youdoas youdoit and to affect what youdoas youdoit. (Doug's use ofallin that prior phasement, requires more exegesis along lines of Mae wan Ho's quanton(coherent,autonomy). Fathom how quantum~all is gnostically "limit separated" by real quantum~adaptationand quantum~affectation as always partial and always enthymemetic. 'Reasons' for this are nearly boundless, so for example, consider that some energy~wellings may remain unaffected (peaqlos only become phase~encoded when a memeorable (re:quantum~memeory) becomes re cognized, consider quantum~entanglement issues, etc. Two pages in Quantonics deal with these issues partially: A 3D Fuzzon, and Doug's fabulous What is Wrong with Probability as Value?). Perhaps even more crucial is that Others' affectationings are evolving as your own holographic process proceeds, latter whose modality is quantum~holographic~evolutionings. This process, this quantum~pr¤cæss, we refer emerscitecting and emerscenturing (E&E). Classically we called it "architecture and manufacture." Latter (classical A&M) presumably can be done in pristine isolation. E&E may n¤t be done in isolation. Classical isolation is another bogus classical notion. For a practical exemplar see our review of Gary Taubes excellent Darwin's Chip.Sparingly, you hear Doug say and you read him write, "epiphany." Our narration has taken us to a quantum~middle~including compenetration of epiphany. Your grasp of this is essential. Essene~tial! Above, under 'classical fractals,' Doug wrote that "...classical objects cann¤t change

per se." What does Latinper semean? It has a purely dialectical, mechanical, formal, ideal, canonical, orthodox, çatholiç, OSFA meaning:simply, and only, it means "by itself."A technical term exists to describe this ideal mechanical, substantial objectivity

per seprerequisite:homeostatic, homeostasis, homeostate, and homeostaticity. Classical objects cann¤t change, they must by theoretical, rational edict...never change: perpetual state, classical absurdity in its most extreme 'form.' Colloquially classical objects areconstant.Now ponder

consequences of thatabsurdclassical edict! Axiomatically, objective reality isconstant. Objective reality mustneverchange in any self~other~affectational~interrelevant evolutionary sense! (Doug uses "absurd" here in a simple way:all classical dialectical thoughts (CTMs) are, in general, demonstrably retarded, so classical objectivism is, in general, retarded:"absurd.")However,

by direct observation and experience, reality. Reality is n¤tdoeschange...realitydoesevolveconstant. Reality is n¤t classical. Reality evolves self~other~volitionally.Reality is quantum.Our epiphany is

:Quantons exist, and Quantonics is real and a valid, though always tentative and partial and enthymemetic, omniscription of reality.Implications of that epiphany are enormous. Objects (as bases of thought and management and politics and governance and 'logic') become inane, genuinely absurd. Quantons move closer to being

betteranalogues of quantum~reality. Quantons self~other change,adapt, and evolve perpetually! It is impossible for a quanton to be classicallyconstant...to be in any classical perpetually stopped 'state!' Quantons evolveab intera~per intera(interrelationshipings,frominterrelationshipingsby:quantons,fromquantons) which themselves are quantons. An intrinsic ofbythatomniscription of a quanton is that quantons self~other change~evolve bothpær sæandpær ihntæra. Objects cann¤t dothat. Let's add a profound memeo to our epiphany:only waves can dopær sæandab intera pær ihntæraquantum~change and ~evolution! And quantum~waves are n¤n objective!Implications include

:leaving classical logics and mathematics, and on interim bases, adopting genuine quantum~coquecigrues and quantum~subjectiv wave~stochastics and theirphysialimplementations in quantum~real m¤dalings. How do we dothat? We learn Quantonics' "Wave Management By Uncertainty™," wMBU™. A crucial step in wMBU™ is learning how to evolve our decision making away from classical dialectical bivalent techniques toward omnivalent quantum~quantiques, especially Poisson~Bracketings.Choose to observe what we describe narratively and visually emulates how any quantum~stagings' brain works

:quantum~holographically, and partially~adiabatically.Every Value interrelationshiping in our visual is a quanton of quantons of quantons(...). Many of those quantons have

quafor quasi~physialquantum~evolution. Con(m)sistency and c¤mpleteness take on n¤væl quantum~semantics now:"Always changes, and changes all." How? All of our quantons are quantized, like this:Then all we have to due to do is add scintillation. See link. Compare classical and quantum, now, top to bottom...and apprise yourself what has been accomplished in moving from classical to quantum:

What has been accomplished here is similar great progress made when Doug showed how Einstein's General- and Special-Relativities were bogus for lack of quantization (lack of innate stochastics) and implicit in quantum~reality whose quantization emersces quantum~relativity naturally,

physially. Simply, flux is crux and quantization is key (a key success enabler).In Quantonics Script

:quanton(¤,~) Simply

pneumaticdeliciousness!Recall how classical fractals were by mathematical and dialectical formal axiom, "Independent." You may easily see how our quantum~fractal is anything but classically 'independent.' In quantum~reality, 'independence' is a bogus classical notion.

Notice some qualities about our

doprocess here:

- never complete in any classical, notional sense,
- always partial,
- always enthymemetic,
- always evolving,
- etc.
Please fathom some of Doug's punness in "

doprocess," vis-à-vis "due process." Doug likes to see extreme SO^{r}ON in running both of those in quantum~complementation on his quantum~stagings' holograms. View quantum~pr¤cæss as perpetual evolution which is an easy way to grasp quantum~reality asalwaysbothpartialandenthymemetic. See SOON.What is Doug's best practical exemplar of this awesome quantum process? A new born baby.

If you are having trouble relating to Doug's memeos of quantum~fractals, you may want to see a recent movie titled simply AI.

If you want some business exemplars, consider: training guide dogs and police dogs. You can imagine others. Always keep in mind that when you are anticipating your own n¤væl quantum business...

"What is unsaid is radically more important than what is said."™A huge impact of this business m¤dæl is that most Value is added during ownership, n¤t during emerscenturing. This quantum~advantage is just one more positive feature of wMBU™.

If you understand how US' GDP is calculated today purely as a pseudo productivity measure of flow of $s, you may be able to grasp how real productivity arises

afterquantum m¤dals are delivered. Genuine, n¤t fiat $, productivity accretes after delivery. In a way, this is what Doug intends when he says, "Real quantum~amelioration." This can take us out of our current, debunked and corrupt Federal Reserve Banking system.There is much more to say here. But Doug has managed to run this into a four day effort. Let's take a rest here and Doug will continue his efforts on "quantum fractals" more gradually over next few weeks and months.

Thank you for reading,

Quantonics, Inc.

Suite 18 # 368 1950 East Greyhound Pass

Carmel, INdiana 46033-7730

USA

1-317-THOUGHT

(21Jul2001 rev - Expect these changes/upgrades to continue for several weeks/months.)

(8Dec2001 rev - Add top of page frame-breaker. Extend and add links to Quantonic Fractals

(21Jul2002 rev - Change QELR links to A-Z pages.)

(26Sep2002 rev - Remediate all quantum comtextual occurrences of 'ensemble.' Remediate 'recursion.' Add 'Quantum Fractals' anchor.)

(26Sep2002 rev - Add more recursion memes under Quantum Fractals.)

(21Apr2003 rev - Add dated red text comment.)

(20Oct2004 rev - Adjust colors and reset legacy red text.)

(15Sep2005 rev - Update classical fractal text.)

(9Dec2007 rev - Reformat slightly.)

(2Nov2008 rev - Replace wingdings and symbol fonts with gifs. Reformat. Reset legacy markups.)

(12-16Apr2010 rev - Add 'how to do' and issues of doing classical and quantum fractals. In response to a query, "How to see quantum~fractals." Correct spelling of 'movie.')

(20Apr2010 rev - Add green text insert under "quantum~fractals.")

(22Mar2011 rev - Add 'Adaptation and Decision Making' and its anchor to text.)

(18Jul2011 rev - Reset legacy markups and add QVH Table and chance links.)

(23Feb2012 rev - Add a quantum~heuristics graphic link to our quantum~cuneiform 'How Quantum SOrONs Self Other Evolve.')

(4Aug2012 rev - Add link to 'Suggested requirements for a novel quantum~mathematics.')

(11Apr2015 rev - Make page current. Reset legacy markups. Adjust color.)