Panchikarana - Sri Adi Sankaracharya (Sankara)-Prakarana-s (pp 163-165).

Panchikarana' refers to the quintiplication process involved in the Advaitic concept of creation. It is a process by which the five
elementary constituents of the universe are said to be compounded with one another to form grosser entities that serve as units in the
composition of the physical universe. The process is also referred to as `grossification'.

Brahman is both the efficient cause and the material cause of the phenomenal world (nimitta karana and upadana karana). The simile used
(not a metaphor) is that of a spider, which weaves its web from the silk, produced from its own body.

Then due to the interaction of the supreme Self with Maya, and the dominant influence of `tamas', there arose `ether' or `space'. Out of `space', the `air' emanated. In due succession, out of the `air', `fire' emanated; and out of `fire', `water' emanated and out of `water', there arose
the `earth'.

Thus these five `tattva-s' (space, air, fire, water and earth) are the first `subtle' elements of creation
(Panchamahabhootani). They are called subtle elements because they exist before they manifest themselves through their association with
the grosser objects of the phenomenal world. Then the `panchikarana' process starts.

1. The `tamas' aspect of each of the five elements divides into two equal parts (parts A and B)

2. One half of each element remains intact. (A remains intact)

3. The other half of each gets divided into four equal parts. (B of each element gets divided into four equal parts).

4. Then, to the A part of each element one part of the B of each of the other four elements gets joined.

5. Then `panchikarana' is complete.

Let' designate space (subtle) = space (S) and space (gross) = space (G).

So, after `panchikarana',

space(G) = ½ space(S) + 1/8 air(S) + 1/8 fire(S) + 1/8 water (S) + 1/8 earth (S)

air(G) = ½ air(S) +1/8 space(S) + 1/8 fire(S) + 1/8 water(S) + 1/8 earth(S)

fire(G) = ½ fire(S) +1/8 space(S) + 1/8 air(S) + 1/8 water(S) + 1/8 earth(S)

water(G) = ½ water(S) +1/8 space(S) + 1/8 air (S) +1/8 fire(S) + 1/8 earth(S)

earth (G) = ½ earth(S) +1/8 space(S) + 1/8 air + 1/8 fire(S) + 1/8 water(S)

 

The five elements that are created as part of prakRiti - space, air, fire, water and earth - three states of matter - solids, liquids and gases and
energy and space. The subtler form of these are created. PrakRiti has three guNa-s or qualities - satva, rajas and tamas.

Satva is the source of knowledge. Satva guna-s of these five elements become the source of JNana-indriya-s or sense faculties. Together they form the source for subtle matter - mind and intellect.


The rajas which is the cause for activity - the rajas aspect of these five emements form the five karma indriaya-s - organs of action at subtler level.

Then comes the grossification of these. In the grossification -panchiikarana starts. Each of the five elements splits into half. Thus space is divided into two parts and similarly the rest of the five.

One half of each remins but other half splits further into four more parts.
The four (1/8th) part joins each of the other elemnts. Thus the space has
its half part plus 1/8th of air, 1/8th of fire, 1/8th of water and 1/8th of
earth - all together forming one complete whole again.

Thus in the pancheekarana each of the unit after the reassembly has half of its own plus
1/8th part of other four elements. These form the basis for the grossification of the universe. From these re-assemboled unit - the
fourteen worlds, plus the gross bodies of all living organims - including gods, humans and animals and plants are made.

This in essense is the panchiikaraNa process.

It is a theory of explaining how subtle all pervading aatma becomes a grossifed forms of many.

Source:

http://www.advaitin.net/Discussion%20Topics/Panchikarana%20and%20Varttika.pdf

http://www.indiadivine.org/content/topic/1054540-want-a-detailed-note-on-panchikarana/

http://www.manblunder.com/2011/05/vedanta-panchikarana.html

Pañcīkaraṇa is an interesting theory. Tamo guṇa of the five elements divides into two halves.
The one half remains as it is and the other half further gets divided into four parts. The half portion that was not divided conjoins with the one fourth part of the other half of another element. The following chart for space, one of the five elements will explain this.
                                                     
The following will explain the formation of the elements:
Space = 50% of space + 12.50% of air +12.50% fire +12.50% water + 12.50% earth = 100%
Air = 50% of air +12.50% space +12.50% of fire + 12.50% water + 12.50% earth = 100%
It is the same for the other three elements also. When this division is complete for all the elements, it signals the completion of pañcīkaraṇa (five fold) of the five elements. When the pañcīkaraṇa is completed, the formation of gross body is also completed.
The scripture Pañcīkaraṇa says, “pañcīkṛta-pañca-mahābhūtāni tatkāryaṁ ca sarvaṁ virād iti ucyate पञ्चीकृत-पञ्च-महाभूतानि तत्कार्यं च सर्वं विराद् इति उच्यते”. It says that virāṭ is the sum total of quintuplicated (five fold) five elements and their effects. It further says, “etat sthulaśarīram ātmanaḥ एतत् स्थुलशरीरम् आत्मनः” which means ‘this is the gross body of the Ātman’. Ātman which identifies itself with the jāgrat state (active state, one of the stages of consciousness) and the sthulaśarīra (gross body) is known as Viśva. The seventeen components that were discussed (series 12) earlier is the subtle body of the Ātman, known as hiranyagarbha. When the Ātman identifies itself with the subtle body during dream state, it is called taijasa.
Bound by the reflection of the Self, māyā hides the Self, which is the cause for both the gross and subtle bodies is known as avyakta. This is the state of unmanifest. This stage is said to be both existent and non-existent, because of the involvement of māyā. During the state of deep sleep, thoughts cease to exist and the intellect begins to take rest, thereby signalling the commencement of the deep sleep state. When the Ātman identifies itself with the causal body and the state of deep sleep, it is called prājñā. When the Ātman realises its true nature, i.e. the Brahman, it is called samādhi, leading to realisation. When the Ātman understands that it is the Brahman only, it is called realisation of the Self or aham brahmāsmi or I am the Brahman.

Tattvabodha thus establishes the identity between microcosm and macrocosm. The individual gross body is called piṇḍāṇḍa (microcosm) and sum total of all piṇḍāṇḍa-s is brahmāṇḍa (macrocosm). The individual soul is nothing but a part of the Brahman and realising this truth is known as Self realisation. Due to the veiling effects of māyā, Ātman continues to forget its true nature.