Sunday, January 22, 2012

Fractal Laws of information


I have published - as a page -  the Laws of Information ; all of which  I have collected, and derived from the fractal.

Like a fractal itself, these laws will/should - over time - grow, develop and form shape .

Friday, January 6, 2012

Fractal Speed

What is the maximum speed a fractal can be produced? 
The fractal is produced at the fractal processing speed (fractal speed), this is the speed at which a discernible fractal shape can be created. This speed also determines the speed of zoom – or magnification into the fractal. It is also the speed of the fractal – wave.
Fractal zoom


Fractal speed can be demonstrated by drawing the Koch snowflake freehand. This is rather slow and timely; a much faster method is with modern computer as shown below. The speed is thus limited by the processing power of production. I have published in early entries on the production of the fractal. The average modern computer (in 2011) cannot produce many more than 7 iterations  –  in one  view or 'fractal paradigm'  – before the computer crashes. To produce more, or see more, we must zoom – forward and into and fractal.
The maximum zoom fractal speed must be 'Maxwell’s'  – speed of light.   
Fractal development

If this is so, then special relativity should also be consistent with the fractal as the fractal demonstrates increasing cost with the more iterations or production. The extra – marginal –  cost, is mass in relativity. See diagram below:  mass or cost limits the production speed.
It maybe that at the maximum fractal speed – the speed of light? –  the fractal is also at a 'perfect' state of superposition where there is no reference points –  and thus no connection to time.


Fractal Uncertainty


(Fractal) Uncertainty
Observing a (Koch Snowflake) fractal (Fig. 1 below) in superposition: position, scale and direction (of growth) of any one triangle, is only ever known with reference to another reference point – another measurement or observation – and since there is no reference to be found in this state of ceteris paribus or isolation, there is only absolute uncertainly – of the above. In a previous entry – fractal ceteris paribus – I explained this fractal feature independant of any knowledge of quantum theory.




Can position be determined - in the above fractal anamations?

Fractal: Wave Particle Duality

 This entry is one of a set of entries on the fractal and the strange (quantum like) nature of them. I use the word quantum because there is no other area of knowledge that comes close to explaining or relating to the discoveries I am making with fractal geometry. Blair 11,03,2013

Wave and particle Duality - and the fractal

The below entry is a discovery, not an explanation. I (intend to) write what I see, and what I expect I have found - I do not pretend to fully understand.

Just as the atom can 'weirdly' be described as being both a particle and as a ‘smeared out’ wave at the same time, so too, as I shall demonstrate, can the fractal be described in such a way  - only for the fractal it is not so weird.

The fractal demonstrating a (discrete) particle:

The fractal is defined by a pattern, object or shape repeating or iterating. The the Koch Snowflake (below) demonstrates this iterating - the triangle represents the particle. The triangle (in the Koch snowflake) is a real - but discrete - object, when grouped or iterated, the group or repeating collection creates or forms a snowflake - just as the many branches (on a tree) make a tree.

There are (in principle) an infinite amount of triangles expanding both into, and out of the point of observation in the fractal (below).

Cross Section of the 'superposition (Koch snowflake) fractal
On the superposition fractal (above), position and scale of any one triangle – or 'particle' – cannot be determined without a reference, observation or measurement. When this observation is made, the superposition fractal (taken from quantum mechanics) 'collapses', the shape is formed, and  the fractal position and scale is known.

The fractal as a wave.

The Koch Spiral: notice the spiral wave and discrete triangles


The (Koch Snowflake) fractal (above) is a wave like object. 
As can be seen that the perimeter of the formed fractal is made-up of an infinity of triangles/'particles' and these together act as or form a wave. When a change is made to one of the triangles (the red dot on iteration 0) and this change iterated, as demonstrated, the wave is revealed. Any change to the triangles/ particles will 'mutate' or change the shape of the fractal and be viewed as a pulse, propagating, cycling round and round every 6 iterations (in the case of the Koch Snowflake), forming, if one were to view a change made to the fractal from a Front Elevation view, a pulse in the form of a classic wave.
  • The wave will range through an infinitely of scales: from infinitely large amplitudes, frequencies, and wavelengths,  – down to, but never reaching zero. 
  • The wave will move or be produced at fractal production speed.
  • There are issues of spin direction too. The spiral can spin in both directions, clockwise and or anti-clockwise. 
I am aware that with this discovery, it maybe deduced that the fractal is some kind of force. 

Logarithmic Spiral - Wave function:
The fractal wave will increase in frequency, and decrease in amplitude and wavelength – logarithmically –  as fractal iterates. The wave is sinusoidal
I can only offer the electromagnetic spectrum as an example of this phenomena. I thus deduce that the electromagnetic spectrum is a fractal phenomena.

Below are images and formula relating to my discovery - these issues  need to be explored:

 Electromagnetic Spectrum
The electromagnetic spectrum extends from low frequencies used for modern radio communication to gamma radiation at the short-wavelength (high-frequency) end, thereby covering wavelengths from thousands of kilometres down to a fractionof the size of an atom. It is for this reason that the electromagnetic spectrum is highly studied for spectroscopic purposes to characterize matter.[2] The limit for long wavelength is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length,[3] although in principle the spectrum is infinite and continuous.  - from wikipedia
source:

Circular polarization





Electromagnetic wave equation



Euler's formula

Standing wave
From a Plan view – the cross section view – the fractal is a standing wave. The attractor is a standing wave.
I have often thought of the economy as being a standing wave activity being the flow.


Fractal Entanglement



This entry I hope adds to the discussion on quantum entanglement.

Fractal Entanglement
The fractal at a state of fractal superposition, and in perfect isolation – with no interference from other fractals – may demonstrate the principle of (quantum) entanglement.  

The 'general' fractal that I have been using to describe our reality in this blog is defined as a pattern the same, but different, at all scales' and best demonstrated by the Koch Snowflake (below).

The Koch Snowflake fractal differs from reality in that it is not 'same but different' at all scales, but is rather an infinity of 'the same but same, at all scales'.
'Same same' as there is no interference from other fractals to change the shape of any of the triangles. As the triangles are – in principle – the same; they are – in principle –  'entangled', or coupled, or connected – at all (time*) scales; linked or 'parented' by the original (iteration 1) triangle. The possibilities of triangle location and position are spontaneous, instantaneous, and infinite; while the formation – the production speed – of the real fractal is limited to the fractal production speed – and this is possibly, the speed of light.
Any change to the parent triangle will instantly change all the infinite 'child' triangles  –  at the speed of production.  
In principle, if the parent triangle is changed –  a dot added to it, for example –  this dot change should be relayed to, and shared by, all the possible triangles, and only ever revealed on observation – at which point the infinite fractal shape is ended. The fractal collapses, and a reality formed.  The dot will be observed – elsewhere – on all triangles relating to that parent.

*In this entangled state – as discussed in another entry on time –  if there is no observation, there is no concept of time. 

Fractal Superposition


The (Koch snowflake) fractal demonstrates superposition:

The (Koch Snowflake) fractal at shape equilibrium - assuming no interference from other and in perfect isolation from other fractals - demonstrates and is at a state of superposition. It shows the infinite positions, the 'same' triangles (or particles, information, or the rules) can be - in a cross section view.

Koch Snowflake in superposition







Fractal zoom: infinity

Fractal Quantum: Intro

This entry introduces a series of entries on the fractal – and ‘quantum’.
fractal-superposition
fractal-entanglement
fractal-wave-particle-duality
fractal-uncertainty

Late last year I – briefly – published an entry on the subject of ceteris paribus and the fractal. As an entry it completed a set of (fractal) explanations for – what I think to be – the three main assumptions of economics: rationality, and perfect information the others – it was an entry I had been developing since the beginning of this blog and I always knew it was a deep and special one. For reasons that I aim to explain in this entry, I paused, and quickly took it down again.
I held it back because I realised – or when it dawned on me – that what I had written (or discovered?) may-well hold a greater significance than just that of economics, and opened – for me – the fractal to the domain of theoretical physics – not that my early work didn’t. The language I was using to describe this fractal in a state of ceteris paribus – a fractal in isolation – sounded (very!) similar to that of the language of quantum mechanics.
“Could it be – I thought to myself – that fractals, quantum mechanics, (and even) relativity are the same thing”? “That the insights I am finding in the fractal – and been recording in this blog, unbeknown – may offer a key, a different way to view the quantum world”?



Straight up I thought – yes; no surprises, it should – it has to. The fractal –as I see it – explains and defines our reality: it is – itself – defined as a repeating pattern ; the same, but different, at all scales; in this case, repeating patterns of 'information' or ‘laws’ – at all scales, including the the quantum scale.
At first it was just this (quantum) isolation that caught my attention, but then it soon grew to include the whole quantum set: uncertainty principle (problems of position and observation), entanglement, and wave particle duality. After a time of thinking – if that weren’t enough –concepts of time, and Special Relativity came to view too.

So, for the last few months I have – as a mere novice – been absorbing as much as I can on the topics of quantum mechanics – and the atom: listening to podcasts, radio show discussions with expert particle physicists, and chemists – over and over again – and also reading, and watching documentaries (all of which, I shall try and list below). 
Common in all these interviews – and to ‘us’ thinkers – are questions of: “Will there ever be found a grand-theory that links the ‘quantum world’ and ‘reality’?” and “Where – or at what scale – does quantum stop being quantum, and reality start”? To these questions, I am now confident – as I will attempt to demonstrate – that the fractal offers an answer. If I may be so bold, to add reply to the commonly ‘repeated’ quote associated with quantum that – “no one really understands quantum, and if you do, you really don’t” – I can now say, with the fractal, I do understand quantum, and it is as real as anything else; as real as the fractal is real – and is no longer so weird as it once was.
It could be, that rather than the fractal offering an explanation of quantum ‘weirdness’; conversely, quantum may offer a proof of the fractal’s reality, and that the fractal is a new universal force, that now demands explanation. 
In the following entries I shall – entry by entry, point by point – continue to do as I have been: developing and deciphering the fractal; only now, I shall be offering insights on topics I thought to be off-grounds, even taboo – that of, particle physics and the like. Aware of confirmation bias – i.e. attempting to create something, where there is nothing – or making quantum fit the fractal; I reply, that it is the fractal that is my study, not quantum. If quantum appears to be similar to fractal – or that the ‘two’ are maybe ‘one and the same’, then so be it, and that is very interesting – even a discovery.  
It has been – strongly – recommended to me that I should publish – through the usual academic process – but I am not in any position to do so, and so have instead opted to continue developing and publishing my findings here on this blog: using the technology of our age and the creative commons. If things proceed, advance, or necessitate, I shall publish (formerly) elsewhere, and at another date.

Podcasts
Prof. Anton Zeilinger, Scientific Director, Institute of Quantum Optics and Quantum Information qualifying what 'reality' is and the implications of this on quantum mechanics research.

Marcus Chown, Cosmology consultant and former radio astronomer, and author of Quantum Theory Cannot Hurt You.


Professor Peter Schwerdtfeger, Centre for Theoretical Chemistry and Physics, Massey University Auckland discusses the fundamental aspects of chemistry in relation to quantum physics.

Professor Christopher Monroe - Bice Sechi-Zorn Professor of Physics..