FRACTAL ECONOMICS

  Demand curve and the de Broglie wave function    I have since published in 2023:  This entry has been hanging over me for some time, and I never published it earlier because I never thought I had it quite right or it never felt complete. Though those feelings have not changed, I have (now) decided to publish what I have, intending that my theory will kindle interest and discussion to further develop it. What really is a demand curve anyway? Do they really exist? The reality may be that they are not real physical, tangible objects but instead show the possibilities of goods and services in terms of price and quantity; as with quantum theory, to produce such a curve invokes the ‘measurement’ problem.   It is as if the demand curve is a superposition of all the possible outcomes, just as in quantum mechanics. My hypothesis: The de Broglie wave function and the (consumer) demand function and corresponding curve are both different manifestations of the sam...

The expanding fractal    I have since published in 2023:  Abstract One of the great questions in modern cosmology today is what is causing the accelerating expansion of the universe – the so-called dark energy. It has been recently discovered this property is not unique to the universe; trees also do it, and trees are fractals. Do fractals offer insight to the accelerating expansion property of the universe and more? In this investigation, a simple experiment was undertaken on the classical (Koch snowflake) fractal. It was inverted to model and record observations from within an iterating fractal set as if at a static (measured) position. New triangle sizes were held constant, allowing earlier triangles in the set to expand as the set iterated. Velocities and accelerations were calculated for both the area of the total fractal and the distance between points within the fractal set using classical kinematic equations. The inverted ...

The Koch Snowflake Spiral 2024: last year, I published, using the following, an interpretation of Quantum Mechanics. https://www.fractalnomics.com/2023/05/fractal%20foundational%20quantum%20theory%20published%20.html International Journal of Quantum Foundations, Speculations. The Fractal Corresponds with Light and Foundational Quantum Problems   Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures On route to understanding if  fractals have a 'wavy' like nature , I finally put pencil to paper and drew what I'd been thinking. I have been pondering what effect a 'mutation' or change to one triangle - a dot at the apex of the triangle as shown below - would have or show on the  iterating  Koch Snowflake. I envisaged that it would spiral to infinity, as shown below. By tracing a smooth curve through the (red) 'dots' series of iterated mutant triangles, I would develop - what looks like - a kind of logarith...

I have since published in 2023:  What is the maximum speed at which a fractal can be produced?   The fractal is produced at the fractal processing speed (fractal speed), which is the speed at which a discernible fractal shape can be created. This speed also determines the speed of zooming in or magnification into the fractal and 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 computers, as shown below. The speed is thus limited by the processing power of production. I have published 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 or see more, we must zoom – forward and into the fractal. The maximum zoom fractal speed ...

  I have since published in 2023:  (Fractal)  Quantum Uncertainty Observing a (Koch Snowflake) fractal (Fig. 1 below) in superposition , p osition, 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 – independent of any knowledge of quantum theory. Can the position be determined - in the above fractal animations?

  I have since published in 2023:  This entry is one of a set of entries on the fractal and their strange (quantum-like) nature. I use the word quantum because no other area of knowledge comes close to explaining or relating to the discoveries I am making with fractal geometry. Blair 11,03,2013 Wave and particle D uality - and the fractal The entry below 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 Koch Snowflake (below) demonstrates this iterating - the triangle re...

   I have since published in 2023:  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 that is the same but different at all scales. It is 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 any triangle's shape. The triangles are – in principle – the same; they are – in principle –  'entangled', or coupled, or connected – ...

  I have since published in 2023:  The (Koch snowflake) fractal demonstrates superposition: The (Koch Snowflake) fractal at shape equilibrium - assuming no interference from others and in perfect isolation from other fractals - demonstrates and is in a superposition state. 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

  I have since published in 2023:  Update: After some 8 years I have finally completed writing up my fractal discoveries.  https://www.researchgate.net/publication/343999170_Making_Sense_of_Light_and_the_Quantum_by_an_Experiment_on_an_Isolated_Emergent_Fractal https://www.academia.edu/43989373/Making_Sense_of_Light_and_the_Quantum_by_an_Experiment_on_an_Isolated_Emergent_Fractal https://vixra.org/abs/2008.0228 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 other was an entry I had been developing since the beginning of this blog. I always knew it was a deep and special one. For...

  I have since published in 2023:  Update: I have published on this blog, read here. I have been having a difficult time recently and am unsure what to do.  What do you suggest? I have taken down my many entries on the fractal because I am afraid they will not stand as an official claim to knowledge. Do I publish here on my own, using the low-cost web technology, or go through the usual costly, slow peer review process? My discoveries with the fractal have led me to - what I believe - a straightforward theory of Quantum Mechanics, or what might be called ' a theory of everything'. When I listen to the 'experts' on quantum mechanics, it is as if they are speaking about the same things I have discovered—but not yet published—in the fractal—everything!: duality, uncertainty, entanglement, time, and relativity. What am I to do? A 'highly' academic colleague has advised me to write articles, publish them, and shut down my blog. On the other hand, yesterda...

Ceteris Paribus - keeping all other factors equal or constant. Fractal Isolation This entry shows that fractals demonstrate that Ceteris Paribus exists in reality and has connections directly to our understanding of reality—even possibly at the atomic scale.   Ceteris Paribus  is a central assumption behind economic models and analysis—and, of course, unbeknown to others, all science itself. It assumes or sets all other factors equal or constant, allowing us to study the pattern of the object in question. Without it, the 'cause' and the 'effect' would not be discernible—or would be confused in the 'chaos'. I often explain to those outside economics that this is our way of achieving a controlled laboratory experiment. This is also seen as the weakness of economics, as we don't (really) live in a 'ceteris paribus' world; we live in chaos. I would strongly argue—again—that this is the weakness of all the 'sciences'. We may have theories, ...