## Posts

Showing posts from 2012

### Koch Snowflake and Fibonacci

This entry states that I looked at whether the Koch Snowflake has a Fibonacci number in it. For some reason, I did not publish the result. In the earlier entry, 'The Fractal Multiplier, ' I noticed that the total area is 1.6 times the area of the first triangle. It is of interest to me (the author), and of my mathematician colleague’s, that the Koch snowflake fractal multiplier is 1.6. This 1.6 is very close to (but not the same as!) the  Fibonacci or Golden ratio of 1.618 .

### Fractal Log Analysis Linear functions

Koch Snowflake Fractal Log Analysis These are diagrams that I created last summer. I hoped that they would shed some light on fractal elasticity, but they didn't. However, I am not finished yet with them. I don't have the time or the more profound knowledge to do a complete analysis.  I am publishing them to show they exist, that this is what I have been doing, and because it is better to have them here than still on my computer. Someone else could look at them and make something of them.  I am sure—and can therefore infer—from their shape and characteristics in this analysis that this is the origin of the classical linear demand functions and linear supply functions— and all this from an understanding of the fractal.  I can only think of the: 'walk like a duck, quacks like a duck'. Linear Area Function, derived from the Koch Snowflake fractal.

### Measuring knowledge elasticity with Youtube

Measuring knowledge elasticity with Youtube  A quick note on something I thought of some time ago. Many YouTube clips are not shown in their entirety, as one clip, but as a series of clips of (around) 10 minutes. It has been interesting to me to note the number of views for each of these 10-minute clips. One might think that the counts should be the same for each, but they are not. Are these counts a measure of the value of the knowledge in the clip? If the numbers remain near constant, one might say the knowledge is elastic—more knowledge can be gained by watching the next. If the numbers diminish, one might say the knowledge is inelastic—more knowledge is not gained by watching another.

### The Fractal Cat

The fractal cat: as opposed to the quantum cat A discussion entry. At what size (or scale) would I have to shrink before my cat would eat me? Venus is my cat, and she is the nicest, calmest cat you can think of. However, I have seen her eat mice—not pretty. Is our relationship all about scale? Is this scale a measure or determinant of power?

### Fractal Time: Absolute or Relative?

This is a discussion entry based on my fractal discoveries.   I have since published in 2023:  The fractal with no observation demonstrates no time.  T he fractal  with observation   demonstrates the passing of time, not absolute time, but relative time. 1. No time: -  A fractal in an isolated superposition demonstrates no time. It is only once a reference point is provided that an observation is made - that time is time. When we have a reference point on the fractal, we 'know' our position. The modern clock itself may be a reference point—without it, we could be anywhere or at any time. Without it, we are lost in chaos. The importance of a reference point in time is just as important as any other reference—it is to 'know'. Absolute time: In this blog, I have recently explored two critical areas of science in terms of the fractal: the expanding fractal (universe) and the de Broglie wave function. In both of these entries, I had to act in some kind of motion, c

### Demand curve and de Broglie wavefunction

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 same thing. This theory w

### Neil Armstrong, Sir Edmund Hillary Letter

I would like to share with you a copy of this letter I received from Sir Edmund Hillary. In early 1996, I wrote to him asking whether he had met Neil Armstrong. At the time, I thought the two of them to be two of our greatest explorers (alive). I recall writing that if you hadn't, then maybe they should. Both continue to inspire me greatly.

### The expanding fractal

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 fractal was

### Fractal Koch Snowflake Spiral

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 logarithmic sp

### Fractal: Multiplier

Development and growth of the fractal demonstrate the ( money and Keynesian) Multiplier. The (Keynesian) Multiplier shows how an initial injection of expenditure into an economic system creates more income. This is because added expenditure sets off additional rounds of expenditure with each and every hand or round this income passes. This principle of 'multiplying' the initial injection can be demonstrated by using the fractal. In the diagram below, income is represented by each triangle's area, and the spending rounds by every iteration of the rule.     The initial injection (iteration 1) is represented by the first triangle, which has an arbitrary area of 1. The next round adds 3 extra triangles, increasing the total area of the snowflake. This (principle) process continues until the changes in the area of the triangle—after each iteration—no longer change the total area of the snowflake. In the diagram above, the total area reaches 1.6  at around the 12t

### 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.

### Fractal Speed

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 must be 'Maxwell’s'  – speed of light.

### Fractal Uncertainty

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?

### Fractal: Wave Particle Duality

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 represents the particle. The triangle (in the Ko

### Fractal Entanglement

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 – at all (time*) scales; linked or 'parented' by

### Fractal Superposition

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

### Fractal Quantum: Intro

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 reasons that