Allan Webber at Marino Rocks May 2016

Repetitive addition and Fractal patterns.

Allan Webber 2017  B Sc, Grad Dip Ed Admin (Adel Uni)

Fractal Chaos generatorI began by saying "Addition is a natural process wherever there is change and singular points with powers that favor their proximity to one another.

This favored zone assumption is the essential driver for continuity, adjacency, sequence and duration. Such proximity can be called cohesion and in any form of chaos not restricted to singularities this term applies.

Cohesion that forms the duad gives us the concept we call addition. So we can deduce that addition is naturally occurring in a natural system. And I contend that we don't need any more components than those I have already given to create our Universe."

Fractals move from abstraction into nature.A man from near the back of the mob raised his arm seeking Einstein's attention. He stood when requested and said: My name is Benoit Mandelbrot. It was me that coined the term fractal and since I did I have struggled with a way to define it. So perhaps it would help if I put forward a definition since you obviously understand its difficulty."

Another man stood up from within the mob and proclaimed, "I am Bernard Bolzano. I spent much of my life arguing for time and motion to be kept separate from mathematics so what you say resonates with me. I also put together original ideas on the topic of continuous functions. May I add my thoughts?"

I knew this man of posthumus fame, who never had the chance to know his work would became the inspiration of many. Words he once spoke come to my mind since they sum up so well the mental place I want my guests to go. "Even in the realm of things which do not claim actuality, and do not even claim possibility, there exist beyond dispute sets which are infinite."

I responded, "Thank you for your offers however as much as I value your contribution my main concern is to bring the ideas together in a way that achieves my personal goals. I want to merge the abstract but beautiful analyses in maths people like each of you have made with the practical mechanics of building a Universe.

I am proposing that fractals are not just mathematical ideas that reflect nature but they form one of the building blocks usable from the very first parts of the Universe's formation. I want to start with the basis of number and show fractals then result without other intervention in any environment. They become the ever-present factor behind the creative designs that follow."

Einstein added: "However,I will keep you in mind and invite you to join me in ensuring he keeps to the logical methods to which we are accustomed.

Inwardly I smiled but left my thoughts unvoiced "Surely Einstein's words are pointless, any errors they claim I make will be part of my fantasy as will be any challenge."

Concept ceries based on number 3 (Triads)I knew what I wanted to show but it was still in words that meant nothing if not backed by illustration.

So although I could have said "Fractals are the spray painting stencils of nature"  I didn't. Instead I continued on my preset path and said "I want to build a logical structure based on how points can evolve using just the assumptions I have already given."

I continued,"Two single points change the number from the singularity that represents non-continuity to a duad and this is the unit of adjacency. But if two can be so linked then there will arise occasions when another will be added by the same process."

This creates a new concept, that of a chain, which is of course a form of sequence.

And the duad is the form of the primal fractal. It is as is every fractal a pattern formed by successive additions of singular parts.

But the thing that transforms the sequence in a chain into the building blocks of a Universe is there being two or more points in that chain that are not unique for then they form another concept, that of enclosure.

Continuity tetrahedral fractal of conceptsAnd enclosures bring about a dramatic change to chaos for with their creation comes the concept of boundaries and constraints on what can or will form within it.

It is repetition of a basic form within a defined boundary that offers us the variant forms of fractals we will observe. Given this basis it is not surprising there is such a close correlation between maths, nature and the cosmos."

An old man stood up and as he did those around him rose as one. The anger in the old man's eyes, the quivering of his hoary beard warned he wouldn't be denied. His challenge wasn't directed only to me but to Einstein as well.

Fractals and enclosures"What have you done with my harmonies, the geometries and all that I knew to be true?" Around Aristotle and his group others began to rise. Astonishingly a few women rose unabashed by their being vastly outnumbered.  I knew the reason for their anger since they had been drawn here not by choice but by the tailwind of my fall. Scooped into my vortex the unrelenting tearing at their long-held scientific faith disturbed their well earned rest.

I had no choice. There was only one means at my call. I fled my dream waking with a shuddering jolt.