Man, the hardware just makes an illusion, after all. Don't get nuts about that or about how hard it is to grip the source of an specific equation/function as if you had to imagine it based on its results instead of how it works in a specific case, binded for a purpose (math alone is steryle but is amazing when joins its functions in a purpose to work as an

**analogy of the nature - in this case, resulting graphical analogy in heterogeneous equations**).

What those funcions have worthing (trigonometric) is that they return something between a range in a fixed way (what comes x goes out y, always), bouncing from up to down (or left/right, back/forth, -1..1, sun and moon, black to white, whatever defined and represented as a - mostly required smooth- transition).

What you see in the screen is a composition resulting from a specific time changing parameters that result in a scene created ( I am not going out of the scope since the "bones" of the issue ARE the mathematical functions). A simulation as how hardware works is no magic but a bunch of tricks and those trigonometric functions are nothing but this:

http://www.youtube.com/watch?feature=player_detailpage&v=s1eNjUgaB-g

ACTUALLY a bounce. ACTUALLY. Other kinds of functions represent (because they act as) other natural phenomenons (as a steady grow in 2 dimensions done by a square or three dimension done by a cube), going parallel (as simulation) to what happens in nature, chained to other functions based on natural results of natural interactions of the aspect (variable) you are seeking for. That is directed/aimed functionality (with functions being its "artifacts", not its purpose - despite being a purpose as language to computers).

You may not grip the math as a plotted dropping results of specific variables flowing thorugh functions to define spatial conditions because it renders too fast. If you could see the rendering not as fast, you could then see how the interactions lead the results into known ways of using trigonometry to simulate movement (riding a bicycle is somewhat like - you know the steps but speed makes it work). Don't fall into the functions as if they were an "identity of a transformation" by its declaration but take it slow to see that every piece of a function is an independent possibility bounded specifically to act as a part of a simulation of phenomenon either in literal meanings (direct rendering) or flow control (function direction/parameter). What you see in an algebric expression is an articulation or an identity to a natural event at last, in its minimal aspect known/identifiable.

There is no physical limit for simulation.

**Don't get functions as fetish without understanding its limits and how they are connected and the pratical purpose.**

The results you see is just the attenuations/vectorizations(perspective adjustments) of the same functions based on another variations, all computed in a way to APPEAR that there is a WORLD being drawn and not just "

**chained reactions of known results based on observed motions in reality that goes in just ONE DIMENSION for EACH VARIABLE**, positioned in a 2 dimensional space.

**2 (even for 3D graphics)**.". Don't grip the world, the simulation is

**PURE ARTIFACT of reality, made by mind**. Don't go believing that there is a magic for "deep simulation" in the functions because there is no deep, just a parameter changing how a variable changes based on a simbology that turns a number into a fraction of another and THAT IS THE MAGIC: A number changing others based on its own value and by that change in especific and isolated variables, shifting up/down, reducing lengths of lines, affecting sizes, TURNING/TREATING X into/as Z, Z into/as Y, Y into/as X and causing the effect of rotation/flipping based on simple substitution (each matrix used can use

**anything as anything**, by any parameters based on any source - anything in this case is NUMBERS that can be vectors/scalars or those "normals" that put z into z, x into x and y into y again

**to close the circus**). I swear again: THERE IS NO REAL TRANSLATION, DEPTH, SCALE, ROTATION or whatever: what you see is a number changing another number to appear a scene, all based on an immitation of what would happen in reality (the "world" is just a relation between functions:

*no matter how beautiful or weird an equation/function may appear because it doesn't work by itself and if the real condition from where it was concepted changes, the equation might change too - the conception of a function is the real art/synthesis, its utilization as graphics is, amazingly,*).

**just artifact of math - in analogy to nature**If algebra is like the sun for you,

**don't look at the sun**. See how it was made and you might understand (the many aspects of reality that math simulates and how they join to result in a variable).

Your vision shall not be the same as the Marionette (I hope) but the handler (who has nothing more than a few strings and sticks but, by his hability, can make a beautiful world to entertain people - math just have numbers and its transformations.. single or chained functions based on nature, or not):

http://www.youtube.com/watch?feature=player_detailpage&v=SPBm8I7hoBQ

Sorry for my way of explaining, might not be good but, may help.