Thursday, 22 May 2008

Physical, mental, psychological, social realms, all are deployed around us fractally.

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.

Tuesday, 20 May 2008

How come the whole is more than the sum of its parts?

In the paper Fractal Memory for Visual Form, in their application of the concept of iterated function systems aiming at constructing fractal objects, which appear as natural-looking images, it is mentioned that

"The resulting image is an attractor for the iterative system. One non-obvious point: the form of the attractor is independent of the starting image. I could have started with any image other than the square, and the Sierpinski Triangle would have resulted."

The fractal object produced, referred to as an attractor, being independent of the starting image? Any chosen object would produce the same attractor? The Sierpinski triangle? Provided that the procedure, the iterated function system, is the same? The iterated function system has a quality of its own? An attribute altering quality? The procedure being more significant than the part that makes up the whole? The particular iterated function will produce a certain form of an attractor despite the difference in the starting object? The iterated function systems have emergence qualities? What are the implications of such thoughts?

The whole, the fractal object produced being more than the sum of its parts. The attributes and properties of the whole different from these of the parts, the reason being the application of the iterated function systems procedures?

And the fractal geometry, that nature is built on, governed by "self-similarity" where the parts resemble the whole?

The human mind mirroring nature employs similar procedures along the lines mentioned below

" ... memory is not a passive list of attributes, but rather is a set of mental procedures. These procedures, when activated, allow a reconstruction of a semblance of the original experience."

Memories stored in reverberating neuron assemblies in the brain as mental procedures, ever ready when activated to construct experience.