MAT 495 Visual Design through Algorithms


E. Anthony Giron





Effects of Randomness on Noise

With each equation just being a series of mathematical statements, and the product produced being the visual representation of what the equation represents, it is clear to see that noise is nothing more than the product of randomness. Insert random elements into an equation and the results are the same, noise.

As such, it goes to show that everything stems from the chaotic elements that randomness integrates into the equation. One example that can be seen is within the Weiner interpolation algorithm. When using this algorithm, in one of the variations that can be played off of it, origins of the starting point for the design are being estimated from being given location points. From these points, it goes into estimating where the process might have begun in order to reach those points. In the fact that it is estimating an unknown, a new random element is brought into the equation. With this random element, noise can be created. At the same time, since it is coming up with a single point, it can also eliminate noise by taking out other possibilities and narrowing it down to one fixed point. Either way, it goes to show how the randomness of finding that point creates noise and as being able to create it, it can also destroy it. At the same time, depending upon other variables around the final points that are being used could state what type and how much noise will be generated. By taking these fixed points, and placing them in an equation to come up with unknown origins, noise has the chance to come about.

Another algorithm that displays the role of randomness would be the sparse convulsion algorithm. With this algorithm, the randomness comes in by varying the number of impulses it has to go through. With increasing the impulses, the greater the randomness of its design will become. The impulses, at the same time are influenced by another variable, deemed voxel, which is the true key to the randomness of the equation. By this variable acting as the key for generating random number of impulses within a certain range, randomness is truly allowed to come into play.

From analyzing the Weiner Interpolation Algorithm and the Sparse Convulsion Algorithm, it seems quite clear that randomness, as being the act of giving results in a non-linear fashion from what was once in a linear orientation, is the cause for noise. Noise, is therefore, nothing more than just the graphical representation of the affects of randomness on equations. Without the random elements, it would not be possible to have noise.

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