Metallic MOS: Difference between revisions
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Each new level of the Stern-Brocot tree introduces the next power of 2 more intervals, but this does not necessarily mean the next power of 2 more generators. Many potential new generators are equivalent to ones which have already been found in shallower levels. Some interesting patterns arise in the counts of truly new generators introduced per level. They are similar but different from one metallic mean to the next: | Each new level of the Stern-Brocot tree introduces the next power of 2 more intervals, but this does not necessarily mean the next power of 2 more generators. Many potential new generators are equivalent to ones which have already been found in shallower levels. Some interesting patterns arise in the counts of truly new generators introduced per level. They are similar but different from one metallic mean to the next: | ||
{| class="wikitable" | {| class="wikitable" | ||
|level | |'''level''' | ||
|golden mean | |'''golden mean''' | ||
|silver mean or isotope | |'''silver mean or isotope''' | ||
|bronze mean or isotope | |'''bronze mean or isotope''' | ||
|4th metallic mean or isotope | |'''4th metallic mean or isotope''' | ||
|- | |- | ||
|1 | |'''1''' | ||
|1 | |1 | ||
|1 | |1 | ||
| Line 1,038: | Line 1,038: | ||
|1 | |1 | ||
|- | |- | ||
|2 | |'''2''' | ||
|1* | |1* | ||
|2 | |2 | ||
| Line 1,044: | Line 1,044: | ||
|2 | |2 | ||
|- | |- | ||
|3 | |'''3''' | ||
|2 | |2 | ||
|3* | |3* | ||
| Line 1,050: | Line 1,050: | ||
|4 | |4 | ||
|- | |- | ||
|4 | |'''4''' | ||
|4 | |4 | ||
|6 | |6 | ||
| Line 1,056: | Line 1,056: | ||
|8 | |8 | ||
|- | |- | ||
|5 | |'''5''' | ||
|8 | |8 | ||
|12 | |12 | ||
| Line 1,062: | Line 1,062: | ||
|15* | |15* | ||
|- | |- | ||
|6 | |'''6''' | ||
|16 | |16 | ||
|24 | |24 | ||
| Line 1,068: | Line 1,068: | ||
|30 | |30 | ||
|- | |- | ||
|7 | |'''7''' | ||
|32 | |32 | ||
|48 | |48 | ||
| Line 1,080: | Line 1,080: | ||
But we don’t find generators for specific means or isotopes in isolation of their other isotopes; it is more helpful to consider the pattern of counts of new generator introductions for the entire family of values for each metal: | But we don’t find generators for specific means or isotopes in isolation of their other isotopes; it is more helpful to consider the pattern of counts of new generator introductions for the entire family of values for each metal: | ||
{| class="wikitable" | {| class="wikitable" | ||
|level | |'''level''' | ||
|golden mean | |'''golden mean''' | ||
|silver mean or isotope | |'''silver mean or isotope''' | ||
|bronze mean or isotope | |'''bronze mean or isotope''' | ||
|4th metallic mean or isotope | |'''4th metallic mean or isotope''' | ||
|- | |- | ||
|1 | |'''1''' | ||
|1 | |1 | ||
|2 | |2 | ||
| Line 1,092: | Line 1,092: | ||
|4 | |4 | ||
|- | |- | ||
|2 | |'''2''' | ||
|1 | |1 | ||
|2 | |2 | ||
| Line 1,098: | Line 1,098: | ||
|4 | |4 | ||
|- | |- | ||
|3 | |'''3''' | ||
|2 | |2 | ||
|4 | |4 | ||
| Line 1,104: | Line 1,104: | ||
|8 | |8 | ||
|- | |- | ||
|4 | |'''4''' | ||
|4 | |4 | ||
|8 | |8 | ||
| Line 1,110: | Line 1,110: | ||
|16 | |16 | ||
|- | |- | ||
|5 | |'''5''' | ||
|8 | |8 | ||
|16 | |16 | ||
| Line 1,116: | Line 1,116: | ||
|32 | |32 | ||
|- | |- | ||
|6 | |'''6''' | ||
|16 | |16 | ||
|32 | |32 | ||
| Line 1,122: | Line 1,122: | ||
|64 | |64 | ||
|- | |- | ||
|7 | |'''7''' | ||
|32 | |32 | ||
|64 | |64 | ||