Frequency class
The frequency class of an object is a measure of its commonness. The frequency class of an object O, in a given set of objects, is defined as x iff the most common object in the set, M, is 2x times as common as O. To wit:
Usage on the LifeWiki
Frequency classes given on the LifeWiki are computed relative to the most common object, block, using data from Catagolue's B3/S23/C1 census:
- FC(object) = log2(occurrences_of_block/occurrences_of_object)
The number of expected occurrences of an object whose FC is known expressed as a percent of all object occurrences in a sample is given by the following formula:
- frequency(object) = 30.9/2FC(object)
- FC is displayed rounded to one decimal place
- Except for an object with an extremely small number of occurrences, an object's FC is highly likely to be stable over time
This metric is used because nine objects (7 still lifes along with blinker and glider) comprise 99% of all object occurrences; the most common object, block, itself comprises 30.9%. The logarithmic function mitigates this skew in the data (see table below).
The frequency class data given in pattern infoboxes on this wiki is taken from Catagolue unless otherwise specified.
The following table is from a March, 2022 Catagolue census containing 302,396 distinct objects with a total of 1,825,795,358,362,300 (1.8 quadrillion) total occurrences, organized by frequency class, where FC Band row n contains objects such that n≤FC<n+1.
This table illustrates how uncommon semi-naturally occurring objects are. For example, the 131,267 objects in band 49 (43.4% of total objects) had a single occurrence and the 36,852 objects (12.2% of total objects) in band 48 had only 2 occurrences.
Distinct Objects | Occurrences | |||||||
---|---|---|---|---|---|---|---|---|
FC Band | Count | Cumulative | Count | Cumulative | Average | |||
0 | 3 | 0.00099% | 3 | 0.00099% | 1,386,516,496,094,870 | 75.9% | 75.9% | 462,172,165,364,956 |
1 | 1 | 0.00033% | 4 | 0.00132% | 160,509,871,835,240 | 8.8% | 84.7% | 160,509,871,835,240 |
2 | 2 | 0.00066% | 6 | 0.00198% | 169,530,166,864,333 | 9.3% | 94.0% | 84,765,083,432,167 |
3 | 1 | 0.00033% | 7 | 0.00231% | 56,166,175,090,709 | 3.1% | 97.1% | 56,166,175,090,709 |
4 | 1 | 0.00033% | 8 | 0.00265% | 17,750,840,203,649 | 0.97% | 98.1% | 17,750,840,203,649 |
5 | 1 | 0.00033% | 9 | 0.00298% | 17,265,010,791,831 | 0.95% | 99.0% | 17,265,010,791,831 |
6 | 1 | 0.00033% | 10 | 0.00331% | 5,717,706,951,779 | 0.31% | 99.3% | 5,717,706,951,779 |
7 | 2 | 0.00066% | 12 | 0.00397% | 6,896,242,512,088 | 0.38% | 99.7% | 3,448,121,256,044 |
8 | 2 | 0.00066% | 14 | 0.00463% | 2,450,443,682,317 | 0.13% | 99.8% | 1,225,221,841,159 |
9 | 1 | 0.00033% | 15 | 0.0050% | 982,376,101,269 | 0.054% | 99.89% | 982,376,101,269 |
10 | 2 | 0.00066% | 17 | 0.0056% | 727,348,485,856 | 0.040% | 99.93% | 363,674,242,928 |
11 | 3 | 0.00099% | 20 | 0.0066% | 533,711,679,075 | 0.029% | 99.96% | 177,903,893,025 |
12 | 2 | 0.00066% | 22 | 0.0073% | 209,261,897,197 | 0.011% | 99.97% | 104,630,948,599 |
13 | 7 | 0.0023% | 29 | 0.0096% | 329,378,744,757 | 0.018% | 99.99% | 47,054,106,394 |
14 | 2 | 0.00066% | 31 | 0.010% | 51,384,468,819 | 0.0028% | 99.991% | 25,692,234,410 |
15 | 6 | 0.0020% | 37 | 0.012% | 72,185,795,980 | 0.0040% | 99.995% | 12,030,965,997 |
16 | 5 | 0.0017% | 42 | 0.014% | 29,646,969,273 | 0.0016% | 99.997% | 5,929,393,855 |
17 | 4 | 0.0013% | 46 | 0.015% | 12,795,789,473 | 0.00070% | 99.998% | 3,198,947,368 |
18 | 7 | 0.0023% | 53 | 0.018% | 11,426,560,754 | 0.00063% | 99.998% | 1,632,365,822 |
19 | 17 | 0.0056% | 70 | 0.023% | 13,452,793,953 | 0.00074% | 99.999% | 791,340,821 |
20 | 18 | 0.0060% | 88 | 0.029% | 6,845,259,994 | 0.00037% | 99.9993% | 380,292,222 |
21 | 22 | 0.0073% | 110 | 0.036% | 4,309,508,239 | 0.00024% | 99.9995% | 195,886,738 |
22 | 27 | 0.0089% | 137 | 0.045% | 2,503,869,239 | 0.00014% | 99.9997% | 92,735,898 |
23 | 47 | 0.016% | 184 | 0.061% | 2,356,344,898 | 0.00013% | 99.9998% | 50,134,998 |
24 | 47 | 0.016% | 231 | 0.076% | 1,173,053,557 | 0.00006% | 99.9999% | 24,958,586 |
25 | 63 | 0.021% | 294 | 0.097% | 783,957,704 | 0.00004% | 99.9999% | 12,443,773 |
26 | 94 | 0.031% | 388 | 0.13% | 559,296,456 | 0.00003% | 99.99995% | 5,949,962 |
27 | 105 | 0.035% | 493 | 0.16% | 316,619,430 | 0.00002% | 99.99997% | 3,015,423 |
28 | 131 | 0.043% | 624 | 0.21% | 191,630,852 | 0.00001% | 99.99998% | 1,462,831 |
29 | 167 | 0.055% | 791 | 0.26% | 123,641,196 | 0.00001% | 99.99999% | 740,366 |
30 | 234 | 0.077% | 1,025 | 0.34% | 88,150,383 | <0.00001% | >99.99999% | 376,711 |
31 | 348 | 0.12% | 1,373 | 0.45% | 64,086,101 | 184,155 | ||
32 | 415 | 0.14% | 1,788 | 0.59% | 38,757,527 | 93,392 | ||
33 | 585 | 0.19% | 2,373 | 0.78% | 27,242,506 | 46,568 | ||
34 | 777 | 0.26% | 3,150 | 1.0% | 18,093,588 | 23,286 | ||
35 | 966 | 0.32% | 4,116 | 1.4% | 11,165,315 | 11,558 | ||
36 | 1,337 | 0.44% | 5,453 | 1.8% | 7,742,091 | 5,791 | ||
37 | 1,862 | 0.62% | 7,315 | 2.4% | 5,411,107 | 2,906 | ||
38 | 2,523 | 0.83% | 9,838 | 3.3% | 3,660,114 | 1,451 | ||
39 | 3,465 | 1.1% | 13,303 | 4.4% | 2,520,856 | 728 | ||
40 | 4,529 | 1.5% | 17,832 | 5.9% | 1,645,756 | 363 | ||
41 | 6,046 | 2.0% | 23,878 | 7.9% | 1,100,748 | 182 | ||
42 | 8,130 | 2.7% | 32,008 | 10.6% | 740,975 | 91.1 | ||
43 | 10,981 | 3.6% | 42,989 | 14.2% | 504,846 | 46.0 | ||
44 | 14,854 | 4.9% | 57,843 | 19.1% | 345,179 | 23.2 | ||
45 | 19,485 | 6.4% | 77,328 | 25.6% | 231,371 | 11.9 | ||
46 | 25,190 | 8.3% | 102,518 | 33.9% | 156,509 | 6.2 | ||
47 | 31,759 | 10.5% | 134,277 | 44.4% | 107,571 | 3.4 | ||
48 | 36,852 | 12.2% | 171,129 | 56.6% | 73,704 | 2.0 | ||
49 | 131,267 | 43.4% | 302,396 | 100.0% | 131,267 | 100.0% | 1.0 |
G1
For extremely rare objects, there might be enough occurrences for a large enough sample size in G1 but not C1. To calculate the frequency class using G1 data, take the standard formula and add 6.3; the number 6.3 was determined empirically.[citation needed] Make sure that the object being checked is one that is not ignored in G1.
See also
- Relative frequency
- Most common objects on Catagolue
- Patterns with specific Catagolue frequency class (category)
External links