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As obvious as it may be i make he point that a 3d graphing programmw such as runiters focusses on the linking aspect of mapping while a 3d fractal generator focuses on the motion part of mapping. So the "surfaces" produced tell me a different story for each programme . Iteration is about motion and motion surfaces or orbit traps i think the correct term might be, and the fractal generators sculpt this motion. The simple rules for sculpting  highlight the complexity of the sculpted motion. More complex sculpting rules may be possible to describe growth motions.

Looking upon newtons third law i am impressed that the notion of "opposite" is not so firmly expressed, nor explained as being linearly opposite or "right" as Newton earlier expressed the motion arising from the impression of a force.Newton i have observed to be every bit as tentative and qualifying as any careful observer should.

Thus i have already redefined the laws in terms of vorticular motion. But it strikes me afresh to observe that the yin and yang symbol describing and designating two fundamentally opposing "forces" in chinese cosmology both small "scale" and large does not indicate a right action but rather a spiral one. This is of interest because the western notion of right action has been influenced much by the cultural transference of information and it would lead me to think that newton in proposing these laws already had infinitesimals in mind. Thus his notion of right was as an approximation to the "true" motion which newton attempted to divine from studies of circular motion.

 Newton was well aware of relative motion and relativity but not able to advance his studies to Einsteins level publically having no cultural need to or relevant data to inform a direction.

The chinese however for some reason not clear to me yet had observed this relationship between opposing principles at all levels and divined a spiral or vorticular relationship. I do know that chinese philosophers did not give credence to absolutes in the western philosophical sense and this may be why they shunned any absolute opposition. In any case the evidence for spirals and vortices in opposing interactions is manifold.

A technical point , but of interest to me is the notion of Archimedian  groups and fields. These are fields that specifically exclude infinitesimals and infinity. Since i was clasically trained my notion of these conceptions have always been based on the notions of bounds and limits. In addition i have induced that the concepts of number and numeral are related but distinct and that mathematics or thinking about iterative processes and procedures and operators and algorithms to describe or construct the same do not require the notion of number, but rather the process of counting or numbering . The cultural iteration +1 being a numeral naming scheme is not infinite but is not bounded above, nor are rational numerals bounded below in the naming of any increasingly smaller fraction.

There is a clear disconnect between notions at this point but that is not unusual or indeed worrying in mathematical thinking that is to say iterative exploration. Discontinuity and boundary differences are normal in "fractals" and self similarity is crucial to identifying these discontinuities and boundaries.

In any case Archimedes was interested in quantization which is the basis of SI units, and for this you cannot have "infinitesimal numerals"  as such nor "infinite numerals". I acknowledge only 1 infinite numeral for computation purposes and that is infinity with
the recently declared numeral nullity as its axiomatic inverse.

Infinitesimals have always meant to me the limit process applied to a region in geometrical space as finer and finer scales are applied. In principle this is Archimedian because i practically have to stop when :sufficiently small to produce no appreciable difference in the result. The use of the term infnitesimal here means i have freedom to continue until such a situation arises. This can be well expressed in archimedian axioms and so leads to no difficulties at that level.

We could define all archimedian Quantity groups as clock arithmetics with various non integer  modulo so for example would represent the radian principle set of real values.

The question is can i live without and ? In the numeral namespace they clearly have a role so my guess is no. The flexibility it gives algebraically for notation is also not a mean advantage.

The notion of proof by contradiction also deserves a note. This really should be named what it is, that is: a test of consistency with the preferred axioms. Thus every mathematical model built with this test should avoid major additional inconsistencies beyond those introduced in the axioms.

Further it is worth pointing out that the models i build of the set notFS are always going to disconnect from and have a region of applicability to the set notFS, this in itself is iterative and leads to the development of fractal models of notFS.

I have learned something today courtesy of phractal phoam phil: solidity does not inhere in space it is attributed to space.

I explain this anecdotally. When i was learning about science iwas given examples of solid liquid and gas to help  form the concepts of solidity liquidity and gaseousness. This of course seemed pretty straightforward and comprehensible. Then i was taught atomic theory. the result of this was that i reviewed my understanding of the liquid and gaseous phase in the following way : solidity inheres in atoms; the liquid and gaseous phase are explained by the kinetic theory of atoms. Thus solidity remained unchanged and in fact spread into the liquid and gaseous phase by attribution of spacial properties via the kinetic theory. Then i was introduced to high energy physics and Niels Bohr's  work and solidity was gradually pared back to protons and neutrons and electrons and massless photons, with the particle wave distinction gradually blurring the description of matter. Solidity was replaced by probabilistic description of position and the newer particles of quarks and eventually colour Quantum Dynamics(QCD). By this stage i had simply forgotten about the concept of solidity having reached out for a concept called "energy" which being indistinct and not well founded remained the linking concept for all new results from high energy physics research. I might as well have called it "Bleh!" for all its use, but it sounded /seemed scientific and utilitarian. However it was not falsifiable and so is in fact tantamount to a faith statement. Nothing wrong with faith statements but they do not tend to advance scientific enquiry.     The fact that it was an ill formed conception i now realise because i could not understand how "space" could be solid. Even though i have briefly flirted with a pixel description of space unrelated to the planck length i could not clarify how that related to motion in space etc, other than by a switching on and off of pixels. The energy conception of space would have plasmas as exemplars but again solidity is inhered in some particle or other.

What dawns on me now is that solidity does not inhere in a particle it is an attribute of space in that it relates regions of space to one another through relativistic properties and not inherent properties of a particle. Thus space can be in constant motion but the relative motions encode relativistic properties which are the attributes we appreciate as rigidity liquidity and gaseousness. This does not require a substance other than space itself but any substance should exhibit the same properties by fractal entrainment to the fundamental properties of space in motion relativistically.

Note on computational consciousness. The computational refers to the manipulation of the molecular and cellular structures within an organism or a structured environment . These structures are at least fractal in that there are structures within structures at different levels of investigation and of different level of dcomplexity.

the arrangement at the dna /rna level allows for a manipulation of the molecular structures through electrical, chemical and hydraulic pressure, and gas pressure feedback feed forward interactions.

At the cellular level the arrangements and connections of cells provides a cellular substrate for a circuit board analogue which provides for an electronic cybernetic system to be expressed, while similarly hydraulic and mechanical cybernetic systems are also established through cellular structure and manipulation. Inherent within these structures is also a chemical messaging system with microbiological inputs and outputs which also form a cybernetic system. These feedback feedforward systems interact so that the hydraulic and gas pressures within the structures and cell structures alter electronic properties within the systems which are then fed back to cascade other alterations in a cybernetic way through a mechanical biological structure in tandem with chemical cybernetic systems .

Without complication the nervous system delivers the main identifiable structures for the computational systems but this is in tandem with the other structures within the  organism. The senses of visual, auditory,gustatory(smell and taste) and kinesthetic/proprioception  are global descriptors of this systems inputs and output systems, which necessarily are complex and iterative and fractal in structure.

Although computational consciousness is a neat phrase it is no different to information processing consciousness or data processing consciousness .

The iterative nature of computational consciousness is clear and the products of that iteration are fractal perception and and construction and concept development. In addition fractal structure is evident in all products of the organism as a whole in particular reproduction.

i have been studying the spaciometry of my garden and it is interesting to look at and derive notions from. Topography is naturally apart of spaciometry and the topography of the structures and objects in the garden is a treat in itself! The topogahical arrangement of forms and structures by juxtaposition  or sequential patterning or relative patterning and structural arrangement is fascinating . And the arrangement of structures within structures and the asymmetry and asimilarity is refreshing. The relationships of growth in structures to the similarity within structures is interesting and the notions of boundaries as applied to complex structures made up of well defined objects which themselves are structured is very fractal. The notions of surface continuity discontinuity regions and spatially oriented objects which are distinct but connected is also exciting . The notions of space filling and dense yet not solid  are also fascinating.

These forms appear by a growth process which is a combination of internal dynamics within the structures modifies by external conditions, very much like the operations within a fractal generator. I can also see the dynamic disaggregation or erosion or degradation of less dynamic forms by dynamic boundary conditions.

It is interesting to note that Euclidian forms simply do not exist because there are no Euclidian lines of points. Even man made objects exhibit a cobbling together of Euclidian ideas which in one explanation of Riemannian geometry makes these object representative of Riemanns hypotheses.

Measurement by equivalence is strongly suggested and twigs and nets of stalks seem natural measuring tools. Orientation is flexible as some structures are rigid and others are motile, and some follow the sun. Notions of twist and rotation and translation are evident and tessellation of a surface is hinted at but indicative of the difference between living and non living  or slowly growing forms. Convexity and concavity are exemplified and many polygonal forms are in evidence as well as polyhedral. Truncated conical forms f varying heights are in evidence as are loxodromic folding and other spiral/vorticular forms for plant stems and the like.

There are no planes only surfaces and consequently 2d forms are an abstraction. However there are very thin 3d forms which have a consistent depth over a surface region which will approximate a plain. Cartesian and polar coordinate systems seem a natural mesh like measurement tool with variable orientation mimicking the natural rotations in some structures. I can establish from each of these types of structure an extension measure and a rotation measure. I can also establish a density measure as a measure of iteration or tessellation  which is commensurate with notions of surface area. I think that a notion of space filling is easy to establish but volume is less obvious because density is so intrinsic to space filling but volume attempts to exclude density. The common notion of volume it is apparent is a surface area bounded space, which is a generalisation of area which is the edge or boundary enclosed space.

In spaciometry i have a chance to define a spaciometric density, which is an apparent notion and axiomatic to spaciometry, but i have to go back to axiom 1 to define it.

The construction of my experiential continuum utilises inate processes and procedural forms, hence my interest in axiomatising parsing and syntax, which i will get round to. It also uses inate forms in fact form is an inate notion derived from as it turns out all the sensory inputs. Form is a synesthesia. We have an extensive-model of the world which gives location information not only by binocular vision but by bin orificial sensation! So location is given by the visual kinesthetic auditory and gustatory and proproceptive sensual systems through processing algorithms in the brain. Kinestthetic systems properly include proprioceptive but i am distinguishing the external from the internal. Interestingly our kinesthetic includes th whisker effect of the hairs on our skin, which also contribute powerfully to location information .

Thus my primary reference system of orientation extension  and rotation relative to the orientation is a conglomeration of the sensory input processed by an evolutionary and possibly revolutionary algorithm process in the brain which the whole organism accepts s a fundamental stabilisation . However alaong with these stimulus response products are also products such as mas, density, surface, form structure etc. The notioins of region and boundary are such products where region uses orientation and a soft focus to give a meaning to its denotation. The soft focus provides a boundary impression without defining a boundary. Boundaries can then be defined or discovered in this region in terns of sharp focus and the particular rods and cones in the eye stimulated by this procedure and aor any other binary type output from the supporting senses.

Mass then refers indiscriminately to the substance being sensed that is space itself. I can now quantify mass by boundarisation and form and structure and surface. Mass can be defined by a numeral representing the count of the structures and forms  and surfaces and boundaries identified within a region

On the face of it a smooth surface may count at 1 form and/or 1 structure within a defined region, but i have to be careful not to confuse abstractions such as planes etc with regions. A surface is only usually one face of a form and special forms should be looked at in their actual not ideal format. Currently i can link mass through Avagadros constant to molecular structures in a form. Spaciometry includes these atomic forms in its conception, but this really highlights the fractal nature of all forms and regions and the structure of a region when boundarised may be analysed in this way to determine a mass.

The profound result for me in developing a spaciometric mass and density is the discovery of magica trigger that gives me a full synesthesia of mass combining the notions to reaify mass.

Considering the gaseous phase of matter and in particular water vapour and clouds i realise that these regions of space have colour, from invisible in the near locality to opacity in tone and rainbow hue. This variation in itself gives me information about mass and density of the gas in the region. If i then include the contribution from smell i begin to realise how pervasive, subtle and powerful the apprehension of mass and density is. simply by smell i can appreciat the mass of a gas in the region i am identifying.