At the heart of the fractal paradigm is the recursive identity.
This is an equation-like form that identifies a label as almost equal to itself, a n unmistakeable procedural expression, and a palpably dynamic equation.
The process of the identity is called recursion or iteration, a simple enough process to understand when presented rhetorically. The rhetorician is able to draw on other sensory modalities such as musical patterns, dance rhythms and poetic motifs to analogise the dynamic behavioural form. Because most mathematics is presented visually in the west it is necessary to warn the reader that mathematics is highly biased and constrained and cut off from its natural roots in human interaction with space, the Shunya field.
The intuitive response to the Shunya field is rhetorical including all art forms, thus to systematically deprive students of that non literal and non verbal information leads to the artificial difficulty in communicating recursion and iteration, but the experience of it in growth or disintegration, or just inane repetitious crystallinity hides the clear kinaesthetic sensation of procedural dynamism.
Benoit Mandlbrot famously draws attention to his innate ability and tendency to synaesthetically appreciate formulae and equations as visual experiences of procedural activity. Thus what appeared visually unchanging could be procedurally dynamic. It was clear to Mandelbrot that these recursive identities were models of large scale natural behaviour and he was drawn to research them by a unique combination of his early research of work inspired by Argnd, Fatou et al, his visual synaesthesia, his knowledge of the infinite loop problem in computing, and a signal interference pattern his colleagues were puzzling over.
Because the signal pattern showed scale dependent similarity it reminded him of the recursive identities he had researched in Europe. Using the infinite loop with control breaks produced mountains of data, which of course he wished to visualise. The graphics capabilities of computers enabled him to plot data as points. The result helped him to visualise the iterated results of recursive identities and to begin to apprehend the relation between simple rules and complex outputs.
With the progress in computing and computer graphics one set became the iconic symbol of this confluence of simplicity in recursive identities, computing, art and natural forms, the Mandelbrot set.
The advent of colour cycling, surface mapping and more flexible palettes lead to this icon taking on a Celtic/cultic symbolic nature of the associated subject named by Mandelbrot as Fractals.
The important thing about the fractal paradigm is that it associates a behaviour with every point in a reference frame! This is fundamentally if ferret to the Newton corpuscular focal system which associated behaviour rhetorically to only specified points. As a consequence action at a distance is not n issue in a fractal paradigm, because the behaviour at every point us specified as n inherent property or behaviour of that space!
Thus an apparent action is in fact an action that is dependent on the procedural process of applying yhe inherent attribute. Thus in a frame every points behaviour is frozen until the next iteration. It is only in dynamic sequential iterative process that the dynamic behaviour across space visualised. In addition the advance in position sensitive palettes are bringing out further dynamical relationships on an iteration basis.
It is clear that the fractal paradigm can model empirically observed behaviours in space, the Shunya field including Undulatory wave behaviours, but the implication is that the laws derived by positing uniform distributions and special point relationships are topological to a deeper fractal relationship. Thus waves appear to undulate through the Shunya field, but in fact the Shunya field behaves in this way in an inherent combinatorial conjugation, and adjugation.
The fate of the universe depends on these inherent combinatorial relations, not in any laws we may topologically deduce from them.
Within the Shunya field universe i am free to generate field vibrations and undulations. This is a fictional freedom, a degree of freedom of choice in an overwhelmingly deterministic external and internal Lagrangian constraint system. My freedom comes through fractal entrainment, for the very vibrations and undulations i create as if consciously, but fictionally so, because the "i " i so glibly announce to the world is a construct of a symbiotic colony of cells, these undulations i call walking, and vibrations i call singing are some of the elementary vibrations of the motor proteins within a cells organelle system