Yes, each transmutation circle is unique and often discovered in secret after much trial and error. The circle, however, is only part of the process. The sigils, seals, shapes, and organization of those markings greatly affect the performance of the alchemical process.
Alchemy (錬金術 Renkinjutsu) is, as it is understood in the Fullmetal Alchemist series, the ancient metaphysical science/mystical art of manipulating and altering matter by using natural energy. This act is known as "Transmutation" and its sequence is usually described as:
Comprehension - Understanding the inherent structure and properties of the atomic or molecular makeup of a particular material to be transmuted, including the flow and balance of potential and kinetic energy within.
Deconstruction - Using energy to break down the physical structure of the identified material into a more malleable state so as to be easily reshaped into a new form.
Reconstruction - Continuing the flow of energy so as to reform the material into a new shape.
The proper application of this craft requires not only a full understanding of chemistry and ancient alchemical theory, but also a sort of natural talent towards recognizing and manipulating the physical objects with energy, which require uncommon levels of intelligence and aptitude. Those remarkable individuals capable of studying and practicing alchemy are known as "Alchemists".
There are many paths by which alchemists can transmute the various substances of the world, with some alchemists being said to transmute by way of the Four Classical Elements (Water, Earth, Fire and Air) and some by way of the Three Essential Principles (salt, sulfur and mercury), but the basic tenet at the very foundation of all alchemy is that of Equivalent Exchange. -- FMA Wiki > Alchemy
The fundamentals of alchemy, the building blocks are available to anyone with the acumen to learn, but it appears to be very difficult and requires both an understanding of the scientific principles as well as an artistic bent and strong spiritual awareness.
The result of the transmutation is not limited by the circle. There is still some element of human interaction or intent to guide the circle. Judging from early transmutation circles created by the Elric brothers, shaping matter was a relatively simple alchemical process, considering the simplicity of the circle (see below).
Alchemists may spend years or indeed their entire lifetimes trying to establish the proper relationships and balances between the elements, their material structures and a desired effect or transmutation.
While the basic form of the circles can be similar, the number of runes, the type of runes, the placement of runes can alter wildly the effects, composition and capabilities of each transmutation circle. This is why transmutation circles can be very detailed, they must account for all potential variables for the singular perfect effect.
Since most alchemists specialize in certain types of transmutation, they may create particular formulas that are translated into transmutation circles. But even considering the transmutation effects, the circles belie the complexity of their creation and their effects. What I mean is given the transmutation circles seen so far, most seem far simpler than expected given what they are able to do with them. This implies perhaps, it is more than just having access to the rune, but understanding how to balance the energy necessary to USE the rune.
For example: this is the rune of the Flame Alchemist, Roy Mustang. This symbol in and of itself is pretty simple.
It is comprised of:
- A specialized flame element mark at the top of the symbol
- An Earth alchemy symbol overlaid by an air alchemy symbol
- Earth and Air are necessary for flame (earth is the fuel, fires need air)
- Overlaid on top of both is the triangle for flame
- Underneath is the symbol of a salamander (believed to be an animal symbol/elemental associated with flame
- Note the boundary circle is not quite containing the elements, like fire tries to escape the confines of the container it is burning in, so does this alchemy try to make the user desire to use his power, more and more.
In the anime, Roy Mustang use of his power seemed to drive him to use it more. The more he used it the angrier and more agitated he became, a side effect of his alchemy and another indicator that the symbols themselves are not enough, there must be knowledge associated with how to use and control the alchemical effects generated, other wise seeing them would be enough to copy them and it isn't.
We can also suspect there is a knowledge element when we remember Hawkeye's father took his notes for Flame Alchemy and inscribed them on her back. These were the notes used to create and master Flame Alchemy. It was considered so dangerous, he did not want anyone to ever have access to them.
Since there is an energy expenditure seen with many of these transmutations, particularly in the case of senior alchemists, equivalent resources must be used to provide the energy needed for the transmutation. It was believed part of the energy for transmutation came from the earth, part from the alchemist, and later from the souls of humans as they leave the material plane.
This would also explain why so much effort was put into finding and creating the Philosopher's Stone. This would allow the Alchemist to have the energy needed without having to create the transmutation circle necessary to control and give boundaries to the powers used.
It was later revealed the reason the Philosopher's Stone worked was because it directly harnessed the souls of the people who died and were trapped during its construction/transmutation.
Variations on a Theme
All transmutation circles are not round. Very complex transmutation structures called arrays are also capable of being used. These structures often utilize energy in unusual ways and are often very powerful and very dangerous. Only the alchemical elite try to create such arrays due to their potential for destruction. The symbols on Scars arms are such an array. (see below)
Transmutation circles can also bind souls to objects transforming those objects in the case of Alphonse Elric and Barry the Chopper, suits of armor, into mobile weapons, capable of movement and incredible feats of strength and durability. These blood seals are vulnerable to damage and if they are damaged or broken the soul is lost.
Barry the Chopper's blood seal