One of the  most basic cognitive science problems is to understand is why the mental function performed by each part of the brain varies as a function of its location within it^.

Any competent model of cognition must
(i) satisfactorily account for the lateralisation of function, eg language on the left hemisphere, emotion on the right hemisphere.
(ii) account for the redistribution of consciousness in split-brain subjects. 
(iii) account for Endel Tulving's biaxial memory mapping. (I)Tulving found memory type variation along a 'vertical' or 'sagittal' axis of abstraction- specifically,  that 'higher', more recently evolved brain centers stored declarative (know 'that') knowledge, while lower, older (in evolutionary terms) brain centers supported procedural (know 'how') knowledge. 
(II) Tulving also found memory type variation along the 'lateral' direction, parallel to the 'coronal' plane which divides the human body longitudinally into dorsal and ventral halves. The left brain hemisphere supported the episodic (INTRAsubjective,  autobiographical, subject-specific) sub-type of declarative knowledge, while the right brain hemisphere supported the epistemological (INTERsubjective, general subject-independent knowledge) sub-type of declarative knowledge.

If the hemispheres could somehow be individually isolated,  each disconnected cerebral hemisphere should by rights contribute equally to overall cognitive function, since, apart from being mirror images, they seem otherwise physically identical*. Therefore, after such an operation, one might reasonably expect that-

Fortunately for science, although not so much for the individuals involved, the two hemispheres can indeed be functionally separated**. These so-called 'split-brain' patients are made by surgical bisection of their corpus callosum, the nerve tract which acts as the 'upper' link*** between the hemispheres. The results are remarkable. Each hemisphere is found to be its 'own person'. This can only be the case if each half has the full complement of neural resources qualitatively associated with higher order subjective phenomenology (ie consciousness) and autobiographical memory. If this set of consciousness-creating resources in each half is spatially distributed in a similar manner to that which existed in the whole, we might then expect each half to also have functional asymmetry, following the heuristic that 'form/structure determines function/purpose'-Ru.3 ^^.

We are in the strange predicament that the physically expected ('normal') symmetrical result, obtained by blind application the above rule (Ru.3), rather than observations of experimental behaviour, ooccurs in surgically altered ('abnormal') patients while the situation in all 'normal' people, for whom the two halves are connected, is that of functional asymmetry. A hypothesis that fits this data must be found.

There are several possible schemes in which mental function varies with location. Way back in the mists of time when Giants (of Psychology) walked the earth, Karl Lashley introduced the engram, a delocalised unit of clinical (ie rat-derived) behaviour. The engram concept is not unlike the delocalised nature of computer software processes, where any file can reside anywhere in physical memory address space, as long as the virtual memory structures are preserved by means of pointers, ie dynamically allocated and tracked meta-addresses. In such cases (universality), function is not tied to hardware resource location. This scheme requires Read-Write access for all memory addresses, as with every commercial digital computer type. It possesses practical portability of function by virtue of large address spaces, which increase exponentially with word length. The running 'image' of the operating system filesystem and kernel fills up the available random-access memory or RAM, starting from the numerically highest address then descending to the lower ones. 

The second possible scheme (uniqueness) is where function varies in a systematic way with location. This is the paradigm used when we make computers or motor cars or any other designed appliance. It is also the rule that applies to some of our internal organs, those we only have one of, such as the heart and the liver. Unique systems are an efficient way of building perfection but are vulnerable to damage, having low or zero fault tolerance.

^^This heuristic must not be applied too simplistically, such as attributing function to the manifest physical structure ('hardware', data transfer and storage device), rather than the latent virtual one ('software', data representation mechanism).
see  Key, B. (2016) Why fish do not feel pain? Animal Sentience 2016.003

 Yet another alternative (ubiquity) occurs when multiple copies of each function are stored at many locations, as in a hologram. In the 19th Century, Hughlings Jackson proposed a version of this system. In Jacksonian memory, multiple 'feedforward' layers cause the mixture of 'positive' and 'negative' symptoms that resulted from localised lesions (trauma or tumours) - see figure 3.1 below. In this architecture, each such layer has some functions that are amplified (+) while others are simultaneously attenuated (-). The behaviour of model systems in which multiple Jacksonian layers are interposed between inputs and outputs closely matches actual observations of both intact and damaged brains, which is why the neuroarchitecture of the TDE is Jacksonian. This neural interconnection scheme represents a biologically plausible type of Read Only Memory (ROM).

Ubiquity is a potential property of 'memoization' schemes. Memoization (NOT a typo of memorisation) is a computer science technique in which a time-consuming subroutine with a small memory footprint is replaced by a much faster, but memory-hungry, fixed data structure, consisting of an array of pre-computed values (a 'lookup' table or LUT). In a LUT all possible symbol values are there, whether they are used (referenced by running programs) or not. This represents a ubiquitous availability of function.  In this highly redundant scheme****, time (CPU cycles) is saved at the cost of space (memory  bytes). 

Clearly, a model which 'fixes' language and consciousness to the left hemisphere fails after callosotomy. The required model must maintain the same or similar spatial pattern of functions when a change of magnitude scale occurs. This is a property of a fractal, a space filling structure which occurs at multiple size scales. Fractals exhibit a kind of ubiquity, since all parts of a fractal pattern are contained within a given region.

Notwithstanding the absurd 'big-brain' hypotheses of the bluebrain/connectome.org believers,  who suggest that the human brain's theoretical performance depends on the total product of (neurons x synapses) = astronomical number of subdendritic nanocomputers^^, the following observations are made about this fractal-

(A) the brain is laterally symmetrical, with left and right 'mirror image' hemispheres arranged on either side of the sagittal (bisecting) plane.

(B) each of its hemispheres seem to be made from four lobes, each of which seem to have a different task specialisation, superimposed upon some shared duties.

(C) the parietal sensory input area is linked to the frontal motor output pathway by a data path which seems to form an inverted loop, consisting of higher level functions. These consist of two types- the so-called 'association' memory in the Temporal cortex, and Limbic/orbito-frontal regions representing emotions and motivation.

(D) the parietal region performs motor as well as sensory functions in a way that is not fully understood, nor widely appreciated. 

^Note, however, that this observation is deemed trivial in almost every other kind of complex system. It seems that the brain's uniformly grey and white colour scheme and  jelly-like elasticity has reduced our belief in our own commonsense. If a system is complex, then that complexity must surely arise by the inclusion of many varied and interconnected sub-systems, regardless of visual appearance (which only predators , surgeons or forensic illustrators can see). 

^^desperation makes normally sensible people act strangely. Facing the lack of a sensible hypothesis about the computational capacity of the brain, and probably under pressure to publish something sensational, some folk have followed the lead of the 'blue-brain' research team and attributed the size of data processing capacity normally exhibited by a whole personal computer to EACH and EVERY neuron's dendritic arborisation (bushy synaptic regions). Of course this ludicrous product yields a number that exceeds the number of planets in the visible universe, and as a convenient side-effect, removes the need for further wonder. "Of course our brains can perform feats beyond the ken of current computers", they say, "each neuron is a computer", is their misguided claim. <sigh>

*except for a slight bulge over the language areas of the left hemisphere, and a small clockwise torsion when viewed from above. 

**in those cases where chronic severe epilepsy threatens life.

***the 'lower' links are the basal structures including brain stem, left and right thalami, hypothalamus, pons and cerebellum.

****Arguably, the high degree of folding of the primate cerebral cortex is due to ROM memoization - trying to fit a large surface area into a limited volume.

John Hughlings Jackson was the first 'modern' investigator to propose that the positive and negative symptoms which result from localised neural injury are produced by a model in which behaviour (output) arises from (a) multiple layers (b) neurons in each layer receive both attentuated (inhibitory) and amplified (excitatory) signals from the previous layer. If a lesion blocks an inhibitory link, a positive symptom (appearance of a new behaviour, eg a tic) may arise. If a lesion blocks an excitatory link, a negative symptom (disappearance of an existing behaviour, eg flat affect) may result. Positive symptoms describe additional behaviours or perceptions that are caused by, or appear after the onset of  the pathology. They  include hallucinations (sensations that aren't real), delusions (beliefs that can't be real), and repetitive movements that are hard to control.  Negative symptoms take away behaviours normally present when healthy , such as the inability to show certain emotions.  

Jackson developed a three-level theory of brain and mind. He claimed that the nervous system is an evolutionary hierarchy of three levels connected by the process of weighted ordinal representation (WOR). This idea (see figure 3.2 below) which is similar to fractalism, preceded the TDE concept of fractal brain structure by over a century.

Observation (B) states that the four lobes of each hemisphere show functionally differentiated roles*. From the split-brain vs normal brain comparison -
(i) when separated, the four lobes in each hemisphere form a cognitive entity which is recognisably conscious, ie capable of limited, though otherwise normal, thought patterns.
(ii) when joined, the two hemispheres also form a unified cognitive entity, whose whole is conscious to the same qualitative degree as each of its halves.

Facts (i) and (ii) indicate that the cerebral hemispheres form a fractal structure, one having fractional dimensions as well as the property of self-similarity w.r.t. scale, just like the branches of a fern, or a snowflake.

By inspection, the brain is made of cells called neurons. It is prima facie a natural structure like a tree, or a snowflake**. For further evidence of the 'fractal brain' hypothesis, we now turn to the 20th Century's most famous linguist, Noam Chomsky, who used the 'paucity of stimulus' argument to suggest that the brain-

By considering Chomsky's opinion in the context of Benoit Mandelbrot's research, the fractal hypothesis is confirmed.

Fractals are self-similar. That means, if the brain is a fractal, the whole brain must look and/or behave in a similar fashion to each of its parts. The brain has two hemispheres, but they each have four parts (P, T, L & T lobes***), not two. To resolve this conflict, the options are as follows-

(i) either these four parts can be grouped into two groups of two parts each, forming a second order (2°) fractal
(ii) or the two hemispheres are paired with other symmetric brain structures, so the whole has four parts, making a fourth order (4°) fractal).

*they can't be properly characterised as computations (functional operations over sets of semantic states) - that has still to be demonstrated.

**or the coastline of England, as Mandelbrot demonstrated. 

***the occipital lobe is not a separate lobe, but a smaller part of the parietal (sensory) cortex. The Limbic 'system' is an anatomically separate lobe, although not usually recognised as such, for reasons which are more historical than medical. 

2° (two part) fractal

Consider Figure 3.3(a). In order to view the local pattern as a 2nd order (2°) fractal, the four lobes at the local level must be reduced (functionally, structurally or architectonically) to two, matching the two cerebral hemispheres. In the most obvious scheme for performing this merger, the Parietal lobe and the Temporal lobe are merged into an ascending, or 'afferent' input hierarchy, while the Limbic lobe and the Frontal lobe are merged into a descending, or 'efferent' output hierarchy. This now satisfies the self-similarity requirement, since the global 'whole' has two parts which match each of the two local 'parts' in a self-similar manner.

4° (four part) fractal

Consider Figure 3.3(b). In order to view the global pattern as a 4 part (4°) fractal, the number of lobes at the global level must be increased (functionally, structurally or architectonically) from two to four, thereby matching the four self-similar local lobes. No changes are needed at the local scale. 

Observation (d) To confirm the choice of the 4° fractal, we now examine the fore-aft decussation between input and output lobes at the local level (ie within each cerebral hemisphere) for a matching function or feature at the global scale (ie across hemispheres, or between cerebrum and cerebellum).

We know that, in animals and humans, the left brain hemisphere governs the right half of the body, and vice versa. This suggests the existence of a lateral (left-right) decussation somewhere in the global data path. This suggestion is confirmed by observations.

This last condition satisfies the functional similarity requirement, therefore the 4° fractal is the pattern that matches observed data, as shown in figure 3.3(b) below.

NOTE- The preferred fractal in figure 3.3(b) is essentially the same information processing model as shown in figure 2.2, ie the GOLEM. 

*John Hughlings-Jackson knew about the functional division between cerebrum and cerebellum in the 1850's, attributing the discovery to Herbart in 1824.