Metallic MOS: Difference between revisions
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The simplest ''metallic generator'' splits the period into two segments which are related by phi. Wilson named this generator “Fibonacci”, after the famous recurrence relation associated with phi, but for consistency here we’ll be calling this the ''golden generator''. | The simplest ''metallic generator'' splits the period into two segments which are related by phi. Wilson named this generator “Fibonacci”, after the famous recurrence relation associated with phi, but for consistency here we’ll be calling this the ''golden generator''. | ||
[[File:Golden generator.png|1361x1361px]] | |||
=== Noble cases === | === Noble cases === | ||
Another way to think about the period is the interval from 0/1 to 1/1. We can find slightly more complex metallic generators by choosing an interval other than the entire period to split into two segments related by phi. For example, we could pick 1/3 to 1/2, giving us approximately 0.419821: | Another way to think about the period is the interval from 0/1 to 1/1. We can find slightly more complex metallic generators by choosing an interval other than the entire period to split into two segments related by phi. For example, we could pick 1/3 to 1/2, giving us approximately 0.419821: | ||
[[File:Noble generator.png|1323x1323px]] | |||
Disclaimer: while these two segments are indeed related by phi, it is not simply by their lengths, as it may appear in the diagram. For now, let it suffice to say that extensions of the golden mean such as this are known as [http://mathworld.wolfram.com/NobleNumber.html noble numbers]. | Disclaimer: while these two segments are indeed related by phi, it is not simply by their lengths, as it may appear in the diagram. For now, let it suffice to say that extensions of the golden mean such as this are known as [http://mathworld.wolfram.com/NobleNumber.html noble numbers]. | ||
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The ''silver generator'' splits the entire period into two segments related by the silver mean, and is approximately equal to 0.292894: | The ''silver generator'' splits the entire period into two segments related by the silver mean, and is approximately equal to 0.292894: | ||
[[File:Silver generator.png|1361x1361px]] | |||
And from the bronze mean, | And from the bronze mean, | ||
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we find the ''bronze generator'', approximately 0.232408: | we find the ''bronze generator'', approximately 0.232408: | ||
[[File:Bronze generator.png|1361x1361px]] | |||
=== Isotopic cases === | === Isotopic cases === | ||
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finding a generator which is approximately 0.414214: | finding a generator which is approximately 0.414214: | ||
[[File:Isotopic generator.png|1361x1361px]] | |||
We’ll be returning to these values regularly, so for convenience, we’ll refer to them as ''isotopes'' of their respective metallic mean, e.g. δ<sub>s</sub> - 1 is the first isotope of the silver mean (and we’ll make no claim as to the scientific appropriateness of this analogy). | We’ll be returning to these values regularly, so for convenience, we’ll refer to them as ''isotopes'' of their respective metallic mean, e.g. δ<sub>s</sub> - 1 is the first isotope of the silver mean (and we’ll make no claim as to the scientific appropriateness of this analogy). | ||
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{| class="wikitable" | {| class="wikitable" | ||
| | | | ||
|period interval | |'''period interval''' | ||
|non-period interval | |'''non-period interval''' | ||
|- | |- | ||
|golden mean | |'''golden mean''' | ||
|golden generator | |golden generator | ||
|noble generators | |noble generators | ||
|- | |- | ||
|beyond golden mean | |'''beyond golden mean''' | ||
|silver generator, bronze generator, etc. | |silver generator, bronze generator, etc. | ||
|aristocratic generators | |aristocratic generators | ||
|- | |- | ||
|beyond golden isotope | |'''beyond golden isotope''' | ||
|isotopic generators | |isotopic generators | ||
|isotopic aristocratic generators | |isotopic aristocratic generators | ||