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{{Glossary}}
{{Glossary}}
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 2<sup>''x''</sup> times as common as ''O''. To wit:
The '''frequency class''' of an object is a measure of its [[common]]ness. 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 2<sup>''x''</sup> times as common as ''O''. To wit:


:[[File:FrequencyClass.png]]
:[[File:FrequencyClass.png]]


==Usage on the LifeWiki==
==Usage on the LifeWiki==
Frequency classes given on the LifeWiki are computed relative to the [[block]], using data from [[Catagolue]]'s B3/S23/[[symmetry|C1]] census.
Frequency classes given on the LifeWiki are computed relative to the most common object, [[block]], using data from [https://catagolue.hatsya.com/census/b3s23/C1 Catagolue's B3/S23/C1 census]:


==Also see==
:'''FC(object) = log<sub>2</sub>(occurrences_of_block/occurrences_of_object)'''
* [[List of common still lifes]]
 
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) = 30.9/2<sup>FC(object)</sup>'''
 
* 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&le;FC<n+1.
 
This table illustrates how uncommon [[semi-natural]]ly 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.
 
{|class="wikitable" style="text-align:center"
! !! colspan="4" | Distinct Objects !! colspan="4" | Occurrences
|-
! FC Band !! colspan="2" | Count !! colspan="2" | Cumulative !! colspan="2" | 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% || <b>99.0%</b> || 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% || <b>99.93%</b> || 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% || <b>99.99%</b> || 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% || <b>99.999%</b> || 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% || <b>99.9999%</b> || 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% || <b>99.99999%</b> || 740,366
|-
|| 30 || 234 || 0.077% || 1,025 || 0.34% || 88,150,383 || <b><0.00001%</b> || <b>>99.99999%</b> || 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 || <b>1.0%</b> || 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% || <b>302,396</b> || <b>100.0%</b> || 131,267 ||  || <b>100.0%</b> || 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.{{cn}} Make sure that the object being checked is one that is not ignored in G1.
 
==See also==
* [[Relative frequency]]
* [[Most common objects on Catagolue]]
* {{CategoryLink|Patterns with specific Catagolue frequency class}}
 
== External links ==
* [https://golhobby.com/ Frequency Class Calculator] and [https://golhobby.com/ Frequency Calculator from FC]
 
__NOTOC__

Latest revision as of 18:23, 6 August 2023

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


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