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Mathematically Beautiful Screen Savers

MBSS Criteria

Many people have asked, "What makes a good MBSS?" Others have inquired, "What are the criteria for a screen saver to be listed on the MBSS site?" As a mathematician first and a software engineer second, I have my own take on the qualifications for what makes a screen saver Mathematically Beautiful (MB).

MBSS products must meet these criteria:

  1. Mathematical Richness: The math in a good MBSS will employ 3D graphics with smooth transitions, splines, gravity, damping and other mathematical constructs. The math will be harmoniously blended into a beautiful display.
  2. Particle Effects: Many products that display 3D graphics use surfaces and texture maps. I feel that this approach simply hides the mathematics under a layer that is rendered by the hardware. A true MBSS will use particle effects -- as such, the math in the product is fully exposed -- revealing something that I call "naked mathematics" wherein the math being displayed is the direct result of the programmer's careful thinking, design and implementation.
  3. Consistency: The product should offer a single coherent theme. The graphics methods should be consistently applied. For example, a product that simulates the atomic interactions in molecules should focus on that one theme.
  4. Continuity: There must be a smooth flow in the particle motion. There can be no jump-cuts from one effect to the next. Ideally, second-degree continuity is employed in the best MBSS products. This implies the use of cubics and 4 * 4 matrices.
  5. Creativity: The product should offer something in the way of originality. Even though there are literally hundreds of fireworks simulations in existence, a product that offers real-time photorealism using advanced lighting techniques will secure its place among products that are universally recognized for their creativity.
  6. Color: The colors employed must not be garish. Color blending and transitions should be smooth.
  7. Completeness: The product should include an easy to setup interface along with online documentation.
  8. Animation Quality: The frame rate must be 24 fps or greater. The animation speed should also be consistent which means that the frame rate should remain the same regardless of the display and effect complexity.
  9. Timelessness: Most graphics products, such as video games, are cool. Their effects offer a temporal beauty. The effects are often anchored within a substrate with a measureable political, cultural, ideological, popular, regional or religious aspect(s). The result: what is cool today is bland tomorrow. As such, these products are not timeless. An effective MBSS will be just as beautiful in a hundred years as it is today -- for the reason that it makes a statement on a single theme with the single purpose of celebrating mathematics. All products can be graded on the Timeless Scale -- where 1 indicates the absolute timelessness of a product and 0 indicates the total disposability of a product. Most screen savers, in particular those of the slide-show variety, have a Timeless Factor very close to 0. Screen savers that employ 'popular' characters wandering about the screen are also disposable, namely for the reason indicated earlier. Timeless products are those that cannot be 'dated' -- they are not associated to any particular period in time.

Characteristics that disqualify a product from being MB:

  • Use of texture maps: This is just my opinion, but after eight years of reviewing screen savers and graphics products, I have yet to be impressed with anything involving texture maps. As I mentioned earlier, I am an advocate of "naked mathematics" wherein particle animation is used to fully express the underlying math in an effect. With rare exception, all of the MBSS products employ particle animation.
  • Palette Animation (PA): The use of palette color shifting is almost always a sure sign of a mathematical vacuum with respect to a screen saver. PA typically results in garish / psychotic colors with no level of intellectual appeal. In very rare cases, a product will use complex math to derive the palette indexing for PA to achieve visual excellence.
  • Lack of attention to the UI and documentation: Sloppy work and oversight in the input parameter user interface and help file indirectly indicates sloppy thinking which portends mathematical errancy.
  • Use of static images and backgrounds: Static images distract from animation flow and continuity.

Objectivity in Mathematical Beauty:

Many people will tell you that 'beauty is in the eye of the beholder.' This is the stance of the subjectivist. One of my goals is that of developing a formal proof to the claim that beauty is objective. Moreover, I intend to show that beauty can be described fully within the strictures of mathematics -- to the effect that, at some later date, one will be able to point to a 'work of art', or any work for that matter, and state the 'Mathematical Beauty Coefficient (MBC)' a value between 0 and 1. The statement can then be backed up by mathematics.

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© 2016  Patrick D. Grengs II  (The Creator of MBSS Light TM)  All rights reserved.