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 2^x 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) = 30.9/2^FC(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

• Frequency Class Calculator and Frequency Calculator from FC