Aggregate structures, Modularity and Pattern formation

Aggregate structures, as i have discussed are of 2 sorts:space forming and sequence forming.

The underlying motion field, which i shall refer to as Shunya, or the void, or even the infinite fractal possibility space, is a relativistic rotational motion field. The consequence of this attribute is fractality at all scales, discontinuity at small scales, periodicity, self organisation,self assembly and probability distributions, with wave dynamical interactivity, regionality, boundarisation, convolution and iterative attributions.

Out of this kind of relativistic motion, emergent properties arise through convoluted interactions , which utilise in local and distant ways convoluted interactional feedback and feedforward loops. These basic distinctions which we have discovered by peering into ourselves and our environment are a tip of the iceberg, but a sufficiently complex enough to explain consciousness as a computational process, and self awareness as a ubiquitous attribute of regionally linked systems.

Our intelligence thus derived, convolutes, through periodicity, back onto self examination and derives further distinctions. Modularity is one of these derivations, which is again found in regionality and periodicity, but we take the idea and utilise it in extraordinary ways. These extraordinary ways we call "sapiens" : which is why we were categorized, as "homo sapiens"

All animates have sapiens, so it is a matter of degree, and we utilise it to an extraordinary degree.Thus modularity becomes the basis of our pattern forming and recognition, both spatially and in intensity.

The uses of these modular patterns are not fixed, but flexible and purpose driven , and the close connection with information storage and retrieval makes it a "system level " distinction. Thus the next level, if you will a system of systems not only has this distinction but is itself designed according to this distinction. Thus the fractal scale property of modularity is evoked, but the flexibility means that the modularity is not necessarily rigid. Thus we may go from a crystalline structure to a more flexible fluid structure to a gaseous organisation al utilising different modularity distinctions and thus pattern forms.

Not only may a pattern of varying modularities exist in spatially intensive regions, but also in combinations of modularity and spatial intensities. thus a system as complex as an animate form , consisting of many differing modularities and pattern forms may exist as well as a purely regular, insanely periodic crystalline form.

However, scale wise the motion field will produce relativistic regional ditributions which show variability at all scales, but which may seem monosyllabic at a particular scale monolithic even.

Cipherism is the term i used to gather together the number worship that runs through mathematics and spreads out into a kind of encoding paradigm, a way of viewing the whole world as quantitative, and based on arithmetical relations or number values. For example: why do we aggregate to derive a numeral? The information the numeral carries is vapid and useless without a referent that is geometrical and spatially intensive. It contains no new information of worth, nor does it enable any new comparisons etc. It is merely another name for the object.

However, then we can use the numeral in a code, as a code or as a way of passing information, and particularly to confuse.

Hamilton started the use of the word set to refer to an ordered set of numbers, or , represented algebraically, a set of ordered variables. But it was Cantor an Dedekind that laid the foundation for modern set theory. Set theory enables us to place cipherism in its proper context and reveals the extent to which mathematicians feel they have to relate everything to the number line concept! Thus cipherism is formalised as foundational to modern mathematics, when in fact it is one aspect of the modularity in our perception of plethoration, and the obsessive devotion to rhythm and variation in hymning.

Aggregation structures can therefore be generally described in set theoretic terms, in which case the relations of union intersection, inclusion,complement etc encapsulate the geometric relations and actions of dynamic spaciometry on regions. Thus group theory is one form of modularity at a general level that enabled spatial and sequential aggregation to be described succinctly.

While listening to Beethoven Pastoral second movement on the radio it was clear to me that i would be remiss if i did not point out that the radio programme was a superb aggregation structure.

The subtlety of aggregation structures is this: motion sequents. Thus any spatial and sequential aggregation whether it be spatial intensity of sound or colour or density or a mixture of all is an aggregation structure devised naturally or by animate "sapiens". This means a soundtrack, a fully featured film, a recipe, a playscript, set of detailed instructions, a novel and a manual are all forms of aggregation structures. the modularity in written scripts is the alphabet, the modularity in musical scores is the pitch keys, the modularity in a film is the subjects of it, and the modularity in my experiential continuum is the general periodicity spread across the whole range of phenomena.

Thus one may resist the pressure and training to aggregate motion sequents in only one."scientific, mathematical" way, and appreciate the artisans mastery of the same topology and spaciometry and spatial intensities as descriptions and solutions of the same areas of interest. For example, the musicality of the attributes of space are downplayed, where once they were fully appreciated.

The aggregation structure which is called a chemical equation has developed on the modularity of the periodic table, and contains within it "deeper", or different scaled modularities based on the atomic structure. We can however see all around us the power and flexibility of this type of aggregation structure and its ability through modularity to enable us to filter down plethoration to a modular structure which we can combine revealingly in a chemical equation. This structure as written performs nothing, but taken as a recipe, a set of instructions for a human chemist it generates a set of motion sequents that alter the spatial intensities in the region of operation of the chemist, and the rgion of convolution of the chemical elements.

This chemical reaction usually has it all, spatial intensity of sound, density and electromagnetic radiation, and of course gravitational reaction as condensation of the product takes place.

We do not usually consider the nuclear reactions in chemistry, but we can if we remember that it is a matter of scaale, and the energies involved also scale. When i say energies i refer to the relativistic motions at that scale.

Aggregation Structure

Parasitic
 architecture
 allows
 the
 creation
 of
 flexible
 structures
 that
 feed
 off
 existing infrastructure
 offering
 solid
 answers
 to
 the
 problem
 of
 structural
 density
 of
 cities and
 the
 need
 of
 temporary
 accommodations.


Additionally,
 modular
 systems potentially 
provide 
forms
 with
 great
 complexity 
out
 of
 simplicity. This
 project investigates
 the
 evolution
 of
 self‐sustained
 parasitic
 structures
 that evolve
 by
 creating
 aggregation
 forms
 well
 adapted
 to
 their
 hosts.

The
 growth process 
of 
the 
parasite 
is 
inspired
 by
 the 
fungal 
colonies 
and
 is 
based
 on 
the
 rules 
of the
 diffusion‐limited
 aggregation
 extended
 to
 support
 force
 analysis
 and
 maintain structural
 stability.


The
 modular
 development
 of
 forms, capable
 to
 adapt
 to
 the
 built
 environment
 without
 affecting
 the
 stability
 of
 the existing
 infrastructure,
 provides
 easy
 and
 low‐cost
 solutions
 for
 extending
 and rejuvenating
architectural
space.


Moreover,
the 
natural
 growth
 process
 of
 diffusion‐limited
 aggregation
 allows
 an
 endless
 evolution
 of
 additional
 spaces
 within
 a
 city
 in respect
 to
 the
 character
 of
 its
 landscape
 and
 human’s
 current
 needs.
 The
 final findings
 propose
 new
 ways
 of
 space
 perception
 and
 introduce
 a
 strategy
 for exploiting 
space.

Rapid prototyping models:

The
 structure
 reached
 equilibrium
 at 
a 
size 
of 
99
 particles,
 of
 which
 45%
 were
 related
 to 
open
 spaces
 of
 a
 total
 1718m3
 and
 2062m3
 of
 total
 closed
 space.
 The
 fractal
 dimension
 of
 the
 structure
 was
 2.6
 increasing
 the
 overall
 dimension
 0.79%

The
 aggregate
 reached
 equilibrium
 after
 72
 particles,
 of
 which
 40%
 were
 open
 spaces,
 and
 had
 a
 fractal
 dimension
of
 2.615.
 The
 calculations 
of 
the
fractal
 dimension
 after
 the 
placement
 of
 the
 parasite
 exhibited
 a
 0.4%
 increase
 providing
 a
 functional
 closed
 space
 of
 1680m3 
and
 an
 open
 space
 of 
1069
m3