My mind has locked into an overdrive mode. The ideas put forward in the paper "Fractal Memory for Visual Form" unleashed a flood which I need to control and release bit by bit. Fractals, as they are referred to as
"irregular geometric objects that yield detail at all scales."
"Unlike Euclidean, differentiable, objects that smooth out when zoomed into, fractals continue to reveal features as more closely regarded."
Fractals, manifest reality unto us only its tip while the bulk of its iceberg is deeply embedded in its fabric rooted to the very beginnings of existence.
As it is stated in the paper
"Benoit Mandelbrot (1983) not only invented the term fractal, but advanced the position that fractal geometry is the geometry of nature."
and to put the point made further, the fractal geometry concept applies itself to all aspects of activity in the world, that goes around us, human and non-human. Physical, mental, psychological, social realms, all are deployed around us fractally.
An idea which becomes evident if we shift our focus in the procedures than the objects reality manifests upon us. Procedures comprised by iterated function systems. The processes being the generating force and not the products.
And as it is mentioned
"our sensory receptors evolved in the presence of fractal objects, bathed in and powerfully shaped by them."
corroborated by the claims about neurons being fractally organised in the brain
"On a descending series of scales, the cell is itself a physical fractal both structurally and functionally in terms of its dendritic and axonic trees, (b) and in terms of subcellular processing both across dendrites (d) and synapto-synaptic junctions."
extend the view that
"that fractal geometry should be adopted in the study of perception and memory for visual form"
to include all aspects of reality being looked upon from the fractal viewpoint.
By concentrating the focus on the iterated function systems which, as it is illustrated
" .. the function part of the name refers to affine transformations. These are functions that alter geometric forms ... transformations like displacement, compression, and rotation."
"These are systems, by which is meant we have a collection of transformations, or 'operators'. The resulting image is the set of images obtained after applying every operator."
all systems, being the collection of transformations, and all changes that systems are undergoing, being looked upon from the perspective of geometric affine transformations. The operators being in a similar sense like the tools a car mechanic uses for each particular engine part, which by applying their action, the mechanic alters the state of the engine. Effects the changes.
Tools, which in a social context are the rules, norms, laws a society has devised to effect the changes among its individual members.
"And they are iterated systems, which means the operators are repeatedly applied to the results of the previous application."
iteration upon the result of the previous application, as it is the case in all aspects of nature's activities and brings about emergence and evolution.