Chaos Theory
Because my All's End novel and any subsequent stories and fan-fictions that I write on Mobius and the multiverse system will define chaos energy a certain way – it was never fully described and chosen, and they are fan-fictions, so give me some space. This deviation is to describe my thoughts on chaos.

Chaos Energy
Chaos energy is the fundamental force that allows the existence of chaos emeralds, chaos adepts, super forms and rings within my Mobius continuity. In the raw state, chaos energy is exactly what it says – chaos, anarchy, pandemonium. The energy that is chaos draws itself from everything, though the change is often impossible to discern, as the energy taken is meant to fuel chaos energy. I do not pretend to know exactly where it came from; I am more interested in current theory and practise.

However, that is not to say that in my spare time I have not pondered the origins, or Theory of Oblivion within the larger picture. My theory on the matter is that like every other dimension, Mobius has its own fundamentals, just as we have the fusion within suns, that the makeup of air is x combined with y etc. For Mobius, chaos energy is fundamental, and is part of everything.

Chaos Objects
This field encompasses Chaos Emeralds, the Master Emerald, and rings.
A chaos emerald is a very basic form of chaos energy storage. Seven emeralds make up the servers, as they are called in Echidna lore, while the Master Emerald serves as the binding link, though what exactly this link does is uncertain to me. But I digress, chaos emeralds are so basic because they allow anyone to use them. However, only chaos adepts, those born with an innate control of chaos energy, are able to use the emeralds without some sort of consequence. When a chaos emerald is used, it gives out power, regardless of who uses it, and those without control over chaos objects therefore cannot use them because they cannot contain the excess energy.

The super emeralds are more powerful versions of chaos emeralds. Each super emerald is approximately seven times the power of a single chaos emerald, so having possession of a single super emerald is equivalent to possessing all seven chaos emeralds. Super emeralds follow the same system as chaos emeralds, though are capable of storing more energy.

Then there is the Master Emerald. The Master Emerald is nigh on impossible to calculate the exact energy, because unlike the smaller servers, it has a sentience within it, the beast chaos, which I believe is there to moderate the energy within the Master Emerald and thus the availability to servers. However, the beast chaos is also as unpredictable as the energy, so any theory on him would prove useless.

The next problem to address is how the emeralds manage to supply a seemingly exhaustible supply of energy. Considering every object can only store a certain amount of chaos energy, it is unlikely that they have such a huge supply of energy that they will not run out of power any time soon. My theory relates back to the master emerald. It is my belief that the Master Emerald draws in a constant supply of chaos energy, more than it can stand, in fact, so the excess energy is converted into rings, more of which will be explained later. This means that the Master Emerald never goes below full power. From there it delivers power to the emeralds, and they are always receiving more power than they need. However a chaos emerald also needs power within it to maintain that link, so that if a chaos emerald ran dry, it would stay dry until someone purposefully delivered chaos energy into it, at which point it would begin charging from the chaos emerald. To define a unit of chaos energy as below I will use the following symbol: (#)
Supply rate of the master emerald: Unknown, estimated to be somewhere close to ten-thousand.
Energy expended supplying chaos and super emeralds: 560#
In short, the Master Emerald only expends a fraction of its total income supplying the emeralds.
@@@@@@@
Energy required by individual chaos emerald: 5#
Energy required by a total of seven chaos emeralds: 35#
Energy supplied to each chaos emerald: 10#
Energy supplied to a total of seven chaos emeralds: 70#
Total excess energy: 35#
Summary: Each chaos emerald receives twice the power needed, and this excess supply rate means that it takes a heavy drain to actually deplete a chaos emerald.
@@@@@@@
Energy required by individual super emerald: 35#
Energy required by a total of seven super emeralds: 245#
Energy supplied to each super emerald: 70#
Energy supplied to a total of seven super emeralds: 490#
Total excess energy: 245#
Summary: Each super emerald requires seven times the power of a chaos emerald, and receives twice that. This excess supply rate that it takes an extreme drain to fully deplete a super emerald.

As aforementioned, the master emerald converts excess energy delivered to it into rings. Each ring holds roughly 0.01# of chaos energy, and receive no power supply, meaning that once a ring is used, it is used up permanently. This means that for every 1# of chaos energy that the master emerald discards, 100 rings are created. To become a ring, the chaos energy undergoes a very complicated conversion process that I do not understand. For more information in that field speak to Miles 'Tails' Prower. This new energy is not only safe to use by all Mobians, due to its more neutral nature, but is also an almost limitless and more readily available supply for chaos-related items. Anything that requires chaos energy to function can do so at a steep cost in rings, due to the energy emitted having the same wavelength as chaos energy. Another part of ring energy that is not fully understood is the timing. When a ring is created, it fades into a middle-zone, an infinite holding pen for rings. From there, a ring will pop into existence randomly, and due to the amount of rings created, it means that often several hundred rings will be created within a space of two to three months. Once a ring enters the Mobian dimension it stays there until used, so rings can be hoarded.

Rings also provide the most stable and versatile source of energy. The most common use of their power is healing, and to this extent, along with standard medical procedure, a Mobian doctor will often give his patient a single ring to help in the healing process. Generally this form of ring actually does not directly heal, rather increases the natural rate of healing by approx. 300% beyond the normal limit. Rings that heal directly can affect the body in other abstract ways so are not recommended for constant use by anyone other than chaos adepts. The other use of rings is for defensive capabilities, specifically shield production. Because this use of rings does not directly interfere with the body, they are allowed repeated use by all Mobians, though because of the process required to change a ring into their specific shields very rarely is a ring shield, other than the standard, employed by the military. It should be noted that chaos adepts do not need these processes, but have a natural skill that changes the ring to the purpose when asked. These are the types of ring shield currently in use:
Ring shield – this type of shield is made of entirely neutral ring energy, so is the cheapest to make and also the best all-round shield.
Fire shield – the rings used in this shield create an orb of fire around the wearer, whilst shielding the wearer from the heat of the shield and to some extent other fire-based and heat-based attacks.
Bubble shield – this shield was developed for divers and underwater operations. Whilst this shield is weaker than a ring shield of equivalent make, it indefinitely allows the wearer to survive underwater, syphoning off oxygen from the water and feeding it into the bubble.
Lightning shield – This shield does exactly what it says. It acts like a standard ring shield, but also has a strong electric current passing across the surface. This shield is the hardest to make and so is in the least frequent supply.
@@@@@@@
Ring shields are generally made using about 5 rings, so use up 0.1# of chaos energy each, by standard military manufacture. Chaos adepts, whom can create ring shields provided they have any sort of ring, also have the ability to modulate the power of the shield, being able to use tens or even hundreds of rings on a single shield if necessary.
There are also three very unique types of ring:
Warp rings, a type of ring that allows travel through space and dimensions, warp rings do not get used up after one use, but are rarer than normal rings to the extent they are used by only a select few. This is one of the few rings that chaos adepts are unable to summon or create.
Inhibitor rings, a type of ring that knows only a very few users. It is used to control the flow of chaos through a chaos adept or chaos-empowered being.
One a ring is used, it fades from being and returns to the chaos flow. Only warp, chaos, world and inhibitor rings do not return to chaos flow.
Eternity Rings: This ring is in effect a specialised warp ring, because it only warps you to the special zone, where the chaos emeralds are sent in the event of destruction.
@@@@@@@
There are two more types of ring to be known:
Chaos rings: These are a set of seven rings that are responsible for saving the life of Miles Prower. Tails absorbed the rings, healing him, but unfortunately for him gave him the curse of Hyperion, the sentience that resides in his Hyper Form. Tails now has to use inhibitor rings to make sure Hyperion does not take over.
World rings: These world rings form parts of Darkspine, a negative transformation available to Sonic. Once Darkspine was brought into being the first time, it was with the use of the world rings, yet only three were needed, so it should be noted that the world rings are infused with a substantial amount of power. However, this meant that the capacity to become Darkspine suddenly became lodged in Sonic, feeding off his rage. Now Darkspine is summoned whenever Sonic gives into his rage and loses control, but the World Rings, the original source of Darkspine, should be kept at a considerably distance from their 'owner'. Each world ring would increase Darkspine's power exponentially with each ring, giving him more and more control and more access to his full abilities.

A final point to be noted is morganite, a substance that is highly resistant to chaos energy, and is a good defence against chaos adept's chaos attacks and any chaos-related ability.

Chaos Adepts
Chaos adepts, as I have mentioned, are beings, specifically Mobians, which have the innate ability to control and resist chaos energy. This allows all chaos adepts to use the chaos emeralds, super emeralds, and master emerald, and all types of ring.
When a chaos adept uses energy, he does not necessarily need to have possession of either a chaos emerald or a ring, already having a minor link to the chaos 'grid' entitling him or her to a slight boost in their natural abilities as normal.
When a chaos adept uses a ring, he uses it just like any other Mobian, and so take no consequence of it, regardless of the amount of rings used, and so is safe from the use of standard ring energy.
When using a chaos emerald, the system is different slightly. Each body has a limit with which they can withstand chaos energy, and for non-adepts this is the 0.000001362# that is background chaos energy, so a non-adept is unable to utilise a chaos emerald even in minor capacity. Chaos adepts have a limited capacity with which they can use chaos energy in their normal form, known as a chaos funnel. For most chaos adepts this funnel is 2# of chaos energy in standard form. However it is also known that chaos adept vulpine species only have access to 1.6# in their normal form, and chaos adept Echidnae have access to 3# in standard form.
When a chaos adept uses chaos energy, specifically from an emerald, he is able to use specific chaos powers, the following are those that are viable to use by all adepts:
Chaos spear – a spear of chaos energy, fired up to long range depending on strength of spear.
Chaos blast – an explosion of chaos energy, targeted at either a set point or centred on the user. In the case of the latter the user is protected from the blast.
Chaos rift – an unpredictable chaos attack, it opens a portal to a pocket dimension, dragging the foe and anything nearby in.
Chaos eruption – the specifics of this attack are unknown, as power and type varies with user.
Chaos control level 1 – an ability that varies from use to use; depending on what the adept wants, it will slow time or allow teleportation.
Chaos control level 2 – An ability requiring two chaos emeralds, it opens a portal that allows travel through time, space, and dimensions.
Each chaos adept also possesses a chaos power unique to him, and those known are shown below:
Lightspeed dash – Owner: Sonic the Hedgehog – Involves sonic curling into a ball and charging his spines with chaos energy, making them tough as diamond, then shooting forward at extreme speeds.
Chaos Tornado – Owner: Miles 'Tails' Prower, vulpine – Literally tampering with the forces of nature, Tails can use this to call up a tornado around himself, though he is protected from within.
Chaos Ram – Owner: Knuckles the Echidna – Using this, Knuckles creates a shield of energy in front of him, protecting him from frontal harm and acting as a battering ram in some cases.
Fountain of chaos – Owner: Shadow the Hedgehog – though not specifically an ability, if Shadow removes the inhibitor rings from his wrists, he effectively then is supplied with the same amount of energy as a super emerald, though it is raw energy, unchanged by emerald status. This ability is dangerous for Shadow, as it drains him significantly when he uses it.
Other unique attacks are commonly possessed by Echidnae in their natural state, but often each Echidna has his own unique set, so I cannot comment on them here.

Chaos and machinery
Unlike Mobians, machinery can channel chaos energy away in within limits defined by the maker, so chaos energy is a viable source for machines, if an emerald can be found. A synthetic chaos emerald, those produced by Miles 'Tails' Prower, are also capable of channelling for machines, due to following the wavelength of the real emeralds, though they can only manifest 3# of chaos energy and are only supplied with 4#, so are much more likely to be drained.

Chaos Transformations
A chaos transformation is essentially an upgrade to a standard Mobian chaos adept. There are a few known levels of transformation:
Super form – Requires seven Chaos Emeralds.
Hyper form – Requires Seven Super Emeralds.
Chaos form – Requires seven Chaos Emeralds, Seven Super Emeralds, and the Master Emerald.
A super form is a more powerful version of a chaos adept, granting them access to level 1 invincibility, the ability to fly, and often a colour change into the bargain. It also widens the chaos funnel, increasing the power of their abilities sevenfold.
A Hyper form gives access to level 7 invincibility, along with both previous advantages. It also widens the chaos funnel, increasing the power of their abilities by a multiplier of forty-nine.
A chaos form is not yet gauged, but powers included an unknown level of invincibility, full access to chaos powers, and the ability to warp reality.
There are a few known flaws with the transformations, specifically Hyper form, which in Miles 'Tails' Prower, has developed sentience, and has to be restrained by a pair of inhibitor rings.

There are also known a number of negative transformations, of negative chaos energy, which are shown below, along with unique transformations:
Sonic:
Excalibur-form: A suit of golden armour, the ability to fly, and the sword Excalibur, formed from the sacred blade Caliburn and able to cut through anything, supposedly. Note: This form is a positive transformation, but is unique to Sonic.
Darkspine: Sonic's rage given form, thus far this form has not needed chaos emeralds to transform, instead transforming when Sonic gives into his rage.
Tails:
Turbo Tails: A form slightly weaker than super form, but only requiring four chaos emeralds, or seven synthetic  emeralds, this is simply Tails' super form, though a weaker version. Note: this is a positive transformation.
Umbra: Not strictly a transformation, due to having a completely separate consciousness, but does not require inhibitors to restrain. Umbra is known to be highly violent and harbours a hatred of everything, including himself.
Death Calibur: The opposite of Sonic's Excalibur form, this uses demonic armour and a great, serrated sword in lieu of the golden armour and invincible blade. Death Calibur, the blade for which the form is named, is still a powerful negative blade, but is not invincible, like Excalibur.
N.B. Tails also has Hyperion, the sentience within his Hyper Form, but again this sentience is not strictly the transformation.
Finally, it should be noted that only Sonic, Tails and Knuckles are capable of Chaos Form, for reasons too complicated to list.

The Mobius Cluster
The Mobius Cluster is the term I use to describe Mobius and all the multitude of dimensions that are alternate realities of Mobius. The key version, Mobius, or Mobius Prime as it is known in context, is the key dimension. Other dimensions, Such as Moebius, have separate versions of chaos energy. Moebius has the Anarchy Bevels, and such the duplicates of the Mobians have their own unique anarchy powers. The most important thing about this is that only the Master Emerald, located on Mobius Prime, has that level of power. Instead, in other dimensions there is only the first level of transformations, and the master gems of the other dimensions only have the rough equivalent power of a single super emerald, though serve the same purpose as the Master Emerald.
However, certain dimensions are capable of using chaos energy in their transformations, such as the Sol Dimension, which is capable of using chaos energy. Moebius, however, is unable to, and in fact the beings of Moebius find chaos energy is toxic, even the background levels, though this is only slight.