The function n() in nakano.py is a complete replacement and enhancement of Jason Summers's Oscillizer, which went offline sometime in April 2021 (but that program's source code was still available). Like Skopje, the whole program started out as a standalone script in Shinjuku before being split into its own repository and is named after a real-world location – Nakano is a special ward of Tokyo bordering Shinjuku (and the repository split occurred during the Tokyo Olympics). In addition to requiring lifelib and NumPy, Pillow is needed to generate the colour-coded maps of cell subperiods that were a hallmark of Oscillizer.

>>> from nakano import n
>>> n("""x = 41, y = 29, rule = B3/S23
... 12boo$12boobo15bo$16bo13bobo$8bo4bo11bo$7bobo4boboo5b3o4bo7boo$16boo4b
... o7boo6bobo$9bo12boo3b5o3boobobo$8boo17booboo3bobobo$8b5o17bo6bo$boo5b
... ooboo22bobbo$obo6bo28bo$oboboo28bo3bo$bobobo12b3o8bobobbo3bo$3bo14bobo
... 8bobbo5bo$bbobbo3bobo6b3o8bobo3bobbo$bbo5bobbo25bo$bbo3bobbobo23bobobo
... $bbo3bo28boobobo$bbo28bo6bobo$bbobbo22booboo5boo$3bo6bo17b5o$bobobo3b
... ooboo17boo$oboboo3b5o3boo12bo$obo6boo7bo4boo$boo7bo4b3o5boobo4bobo$15b
... o11bo4bo$8bobo13bo$9bo15boboo$27boo!""")
p96 oscillator – xp96_0ggy142ky0oggy1gk2gb3wg8gz34jc2mx7f266x23y011xoo8usy1ggzwvwg608k0sy4sksy2g0hxm2cj43zcis346wgo0ggyc302106gwvzy3g3n1110g0ooy0ckgg0664vex643siczy41xcd042y41y0242
Symmetry C1 (temporal C2_1), mod 48
Cell periods:
p96 – 114
p48 – 1
p12 – 56
p8 – 84
p4 – 56
p3 – 88
p2 – 12
p1 – 72
Population 177–240, average 210.77
411 rotor cells (114 full-period), 72 stator cells, 483 total
Volatility 0.8509 (0.2360 strict)
Heat 115–196, average 162.33
Temperature 0.3361 (0.3950 rotor)
Bounding box 41×33 = 1353
Rules B3/S23-k – B34q5c6ci/S234cy6i7e (OT B3/S23)

p96 – ffffff
p48 – 1c92cd
p12 – 0ab87b
p8 – e86075
p4 – f8f290
p3 – ba4117
p2 – d91e9b
p1 – 000000

Running the above command also produces this image:

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Nakano provides all the features of Oscillizer and has the following improvements:

• Instead of an RLE an apgcode can be provided.
• Periods, pattern sizes and number of distinct subperiods are essentially unlimited (Oscillizer had a limit of p300, 400×400 and 10 subperiods).
• Spaceships are also acceptable input (i.e. Nakano can handle any periodic object). In that case a subperiod map will not be produced, but relevant statistics are still computed.
• Any isotropic rule not containing B0 can be used. The rule to use can either be specified in the RLE or through the rule= parameter of n().
• The image size can be changed using the scale= parameter in n(); image output can be disabled by setting scale=0. Where that image gets saved is also configurable using the outfn= option.
• Statistics of interest to contemporary cellular automata enthusiasts, like mod and symmetry type, are computed alongside the traditional ones.

n() is a convenience function for the command line, interfacing with the function analyse(pat_string, rule="b3s23") that should be used when many patterns need to be analysed together. The latter function returns a dictionary with the following string keys:

Key	Value
p	The overall oscillator period. There may be no cells with this period – their presence or absence is indicated by strict volatility (see below).
dxy	A pair of integers representing displacement in the x and y directions per period.
apgcode	The pattern's apgcode.
syms	A triple (base symmetry, temporal symmetry, mod). The first two elements are individually one of the 16 possible "official" symmetries that may be specified in an apgsearch (excluding D8_+2 which Conway's Life does not respect). Base symmetry only looks at individual phases while temporal symmetry considers all of them together; mod is the least number of generations for the pattern to reappear, possibly under a transformation. There are 43 possibilities for the first two elements together (see table below).
pops	List of successive populations of the object, of length p. The presence of this field allows more complicated statistics to be performed on the population (standard deviation, etc.)
popstats	A quadruple (minimum population, maximum population, average population, sum of populations across a period). The last element does not convey any further substantial information – the average population is a standard floating-point number, so the last element allows more accurate computation of the average population should such accuracy be desired.
heats	List of successive heats (births + deaths) of the object, of length p.
heatstats	A quadruple (minimum heat, maximum heat, average heat, sum of heats across a period). See the descriptions of pops and popstats for justification of the seemingly extraneous data.
bb	Measurements of the bounding box: (width, height, cell count [width × height]).
rules	A quadruple (isotropic minrule, isotropic maxrule, outer-totalistic (OT) minrule, OT maxrule). The last two entries are None if the pattern does not work in any OT rule.

The 43 possible combinations of base and temporal symmetries were enumerated in Dean Hickerson's oscillator stamp collection:

Base symmetry (mod = period)	Half-period temporal symmetries	Quarter-period
C1	C2_1, C2_2, C2_4, D2_+1, D2_+2, D2_x	C4_1, C4_4
C2_1	C4_1, D4_+1, D4_x1
C2_2	D4_+2
C2_4	C4_4, D4_+4, D4_x4
C4_1	D8_1
C4_4	D8_4
D2_+1	D4_+1, D4_+2
D2_+2	D4_+2, D4_+4
D2_x	D4_x1, D4_x4
D4_+1	D8_1
D4_+2
D4_+4	D8_4
D4_x1	D8_1
D4_x4	D8_4
D8_1
D8_4

The following fields are only computed for oscillators (and still lifes, which are p1 oscillators):

Key	Value
cellperiods	A dictionary mapping active cells (those positions that are ever alive) to their subperiods. Cells which are alive in the provided pattern have their subperiods negated; this subtlety is used to mark alive cells for the image.
cellpcounts	A dictionary mapping occurring cell subperiods to their corresponding frequencies.
cellstats	A quadruple (rotor cells, stator cells, active cells, strict (full-period) rotor cells). The stator consists of those cells which are always alive, with the remaining active cells forming the rotor.
volstats	A pair of floats (volatility, strict volatility) representing the proportion of (strict) rotor cells to active cells. The latter element is not provided by LifeViewer, which was one motivation for writing Nakano.
tempstats	A pair of floats (temperature, rotor temperature) representing the proportion of heat to active (rotor) cells. These two elements are also not provided by LifeViewer.

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For auditing purposes the script that generated the mooreconfs array, essentially a lookup table mapping neighbourhood configurations to Hensel codes, is included as mooreconfgen.py. The function minmaxrule(), accepting a lifelib Pattern and a number of generations, is not limited to periodic objects and may be used for any pattern whatsoever – the only condition is that the provided rule and number of generations be of interest.