Expanded Search For Pattern

This selects the type of search you want to perform:

• Image lets you enter a pattern image, in any of several different formats, find the pattern that matches that image. The position and orientation of the pattern is not important. For oscillators and spaceships, you can enter any phase.
• Simple lets you search a pattern by name.
• Advanced lets you search a pattern by name and/or certain common properties.
• Detailed is like Advanced, but also includes less common properties.
• Ultimate is like Detailed, but also includes an image.

This selects the cellular automata rule that contains the pattern(s) being searched for. This is normally Life, but you can also select one of several other rules:

• Any searches all rules simultaneously.
• Life is Conway's Game of Life, the default rule.
• B2/S2 is an extremely explosive rule.
• B34/S34 is an interesting rule, once considered a viable alternative to Life, but that has since been determined to be too explosive to be very useful.
• Niemiec's rule 1 is a rule that features several natural spaceships that move at different velocities and directions.
• Niemiec's rule 0 is a less interesting rule, but it includes two additional unusual spaceships.

This selects whether expanded object list is loaded:

• When this is unchecked, this behaves identically to the normal search function, where around 10,000 items (most with syntheses) can be searched.
• When this is checked, an approximately 100,000 additional items (without syntheses) can also be searched. Searching takes longer, but can at least identify obscure items.

Select the name you want to search for. Case is not important. Only letters, digits, and periods are important. Other characters that may be used in names (e.g. spaces, -, #, $) are ignored (e.g. "preblock" matches the name "pre-block").

A * anywhere in the name matches zero or more characters, e.g. "*block" matches anything that begins with "block", "block*" matches anything that ends with "block", and "*block*" matches anything that contains "block". These behave just like the selections in the Advanced Search selection box. But you can also specify more complicated behavior, e.g. "block*ship" matches anything that begins with "block" and ends with "ship", and "*block*block*" matches anything that contains "block" twice.

The ~ character can be used to separate multiple names, and means "and not". For example, "~*block*" means anything that doesn't contain "block", while "*ship*~*block*~*boat*" means anything that contains "ship" but not "block" or "boat".

The ; character can be used to separate multiple names, and means "or". For example, "*block*block*;*ship*" means anything that contains "block" at least twice, or "ship" at least once.

This selects what category of pattern you want to search for:

• Any matches all patterns, regardless of category.
• Still-life matches objects that repeat, and have a period of 1, i.e. no births and deaths.
• Still-life (difficult only) matches only those still-lifes from 15 to 17 bits that were on the list of difficult-to-synthesize ones that were the last for which syntheses were developed.
• Pseudo-still-life matches pseudo-objects that repeat, and have a period of 1.
• Oscillator matches objects that repeat, and have a period of more than 1.
• Pseudo-oscillator matches pseudo-objects that repeat, and have a period of more than 1.
• Spaceship matches spaceships: objects that repeat, but are translated in space when they do so. This also includes pseudo-spaceships (pseudo-objects that behave similarly), and flotillae (groups of two or more traveling in tandem).
• Wick stretcher matches wick stretchers: spaceships that leave output behind them that consists of an fixed number of ever-growing objects, and constantly increase in population.
• Puffer matches puffer trains: spaceships that leave output behind them that consists of an ever-increasing number of objects, and constantly increase in population.
• Gun matches spaceship guns: oscillators that produce spaceships that escape, and constantly increase in population.
• Breeder matches breeders: patterns whose population increases quadratically with time.
• Constellation matches collections of two or more stable, oscillating, and/or moving objects and/or pseudo-objects.
• Methuselah matches small patterns that are not stable, but that run for a long time before stabilizing.
• Not quite stable pattern matches patterns that aren't quite stable, but that closely resemble other patterns that are.
• Patterns with multiple names matches any pattern that has two or more listed names. This frequently happens for larger still-lifes that have descriptive names as well as their numeric designations. It also happens frequently for common objects that are independently discovered or named by different people.
• Patterns with multiple synthesis files matches any pattern that has two or more synthesis files. This can happen in one of three circumstances. Some very large (or difficult to synthesize) objects may have multiple syntheses separated into different files. Many methuselahs that produce large results, especially those that release multiple gliders, have one file showing multiple syntheses, and another containing only one, that allows the methuselah to be run to completion without multiple copies interfering with each other. Finally, some patterns have additional properties that are best illustrated in a separate file (e.g. the Queen bee's ability to eat gliders in many different ways).
• Patterns with multi-color syntheses matches any pattern that has syntheses in multi-color Life.

Each pattern appears in only one category, except the last four, that all include patterns from other categories.

This selects the base population of a pattern, which is the population in its minimum phase.

This selects the maximum population of a pattern. This can be infinite for infinitely expanding patterns. For methuselahs, this is the maximum population of its final census.

This selects the ratio of minimum to maximum population. This is at most 1, but may be zero for infinitely expanding patterns.

This selects the average population of all phases of a pattern. This can be infinite for infinitely expanding patterns. For methuselahs, this is the average population of all phases of its final census.

This selects the number of gliders needed to synthesize an object. It can be a number, or one of these:

• Known describes patterns for which it has been shown that they can definitely be synthesized, but for which no synthesis has yet been attempted. This can currently includes 15- and 16-bit still-lifes, 17-bit pseudo-still-lifes, and period-2 pseudo-oscillators from 17 to 19 bits.
• Unknown describes patterns for which no synthesis is yet known. Such patterns are listed with glider counts of x in pattern lists. This is actually equivalent to ≥ x and also includes partial syntheses.
• Partial describes patterns for which a partial synthesis exists, based on a predecessor that does not yet have a synthesis. This is equivalent to > x.
• TBD describes patterns for which no synthesis has yet been attempted. It is not known whether syntheses exist using currently known techniques.

You can also selects the number of gliders required to synthesize a pattern, relative to its population. It is used to qualify how expensive a synthesis is.

If the Range check box is checked, only syntheses that have a range of different values are matched. Otherwise, ranges match the lowest value within the range.

This selects the period of a pattern. This is the number of generations it takes to return to its original state (possibly translated). For patterns with multiple components, this is the GCD of all components taken together. For infinitely expanding patterns, this includes both the generator (i.e. gun or puffer) and the resulting output. This can be infinite for patterns that expand infinitely in an irregular fashion.

This selects the modulus of a pattern. This is the number of generations that it takes for the pattern to return to its original state, regardless of rotation or reflection. This is the period for most patterns, but can also be period/2 for patterns with glide symmetry, or even period/4 for asymmetrical patterns that rotate 90 degrees four times each period.

This selects the frequency or rarity of a still-life or oscillator. Frequency is always a small real number for the 152 measured objects, while rarity (its inverse) is a large real number. It is listed as Unknown for all others. This is irrelevant for all other object categories, and is N/A for those.

This selects the velocity of a pattern, e.g. how far it moves in each period, divided by the period. This is zero for most pattern categories, and a non-zero number between 0 and c for spaceships and puffers. In most rules, this cannot exceed c/2 for orthogonal movement (although it can reach c in B2/S2). In most rules, this cannot exceed c/3 for diagonal movement (and it cannot exceed c/4 in Life).

You can also select the direction of movement. This can be one of:

• Any matches patterns that move in any direction.
• Orthogonal is for patterns for which movement in in one axis only.
• Diagonal is for patterns for which movement is by the same same amount in both axes.
• Oblique is for other patterns, i.e. those that move in both axes, but a different amount in each. These are extremely rare.

(Velocity is always along the major axis of movement; e.g. an oblique (2,1)c/6 spaceship would be indicated by 2c/6, or more simply, c/3.)

This selects the T.T.S. (time to stabilize) of a pattern. It is zero for all periodic patterns, and non-zero for methuselahs. It is infinite for patterns that expand without limit without ever reaching periodicity.

This selects the E.F. (evolutionary factor) of a pattern. This is the time to stabilize divided by the initial population. It is zero for all periodic patterns, and non-zero for methuselahs. It is infinite for patterns that expand without limit without ever reaching periodicity.

This selects the Influence of a pattern. This is the number of cells whose neighborhoods are ever affected by the pattern, i.e. all cells that are ever alive, or that are dead but adjacent to other cells that are ever alive.

This selects the Minimum Density of a pattern. This is minimum population divided by the influence. This is always a value between 0 and 1. In Life, this must be less than ½ for still-lifes and period-2 oscillators. It can equal ½ for agars of these, but this program does not show such infinite patterns. It can also be unknown for some large patterns whose exact populations have not yet been recorded.

For patterns whose population changes, average and maximum densities (i.e. average and maximum populations divided by influence) are also shown. Average density for period-2 oscillators cannot exceed ½ but maximum density can.

This selects the heat of a pattern. This is defined as the average number of unstable cells in each generation. This is zero for still-lifes and pseudo-still-lifes. It can be infinite for infinitely-expanding patterns, such as guns, and puffers that leave non-still objects. It is unknown for a few large spaceships. For methuselahs, this is the heat of the final census

This selects the temperature of a pattern. This is defined as the heat divided by the population, or total number of unstable cells in all generations, divided by the total populations of all generations. This is a similar measure to heat, but scales with population, so it is possible to define it meaningfully even for infinitely-expanding patterns. (This is similar to the corresponding measures from physics; doubling the size of an object doubles its heat, but does not alter its temperature).

This selects the volatility of a pattern. This is defined as the number of rotor cells divided by the number of rotor plus stator cells. This is zero for still-lifes and pseudo-still-lifes. It is a non-zero number between 0 and 1 for for oscillators and pseudo-oscillators. It is always 1 for spaceships. For infinitely-expanding patterns, this value is dominated by that of the expanding output. For methuselahs, this is the volatility of the final census.

This selects the strict volatility of a pattern. This is similar to volatility, but only considers the cells that oscillate at the full oscillator or spaceship period, rather than all rotor cells. It is defined as the number of full-period cells divided by the number of rotor plus stator cells. This is equal to volatility for still-lifes and pseudo-still-lifes (for which it is also zero), for all oscillators and spaceships with prime periods, and for totally volatile oscillators of other periods.

You can also select the ratio of strict volatility and volatility. This also always varies between 0 and 1.

This selects the squareness of the smallest bounding box, which is the ratio between its height and its width. This is always 1 or smaller.

This selects the smallest bounding box of the pattern. This may be smaller than the bounding box of the phase with the smallest population.

This selects the squareness of the largest bounding box, which is the ratio between its height and its width. This is always 1 or smaller, and may be 0 for patterns that expand infinitely in one dimension. It is defined properly for patterns that expand infinitely in two dimensions, because they may expand at different rates (for example, the B heptomino releases two gliders escaping at right angles, expanding twice as fast in their common direction, so its squareness is ½.)

This selects the largest bounding box of the pattern. For methuselahs, this is the largest bounding box of the final census. One or both dimensions may be infinite for infinitely expanding patterns.

This selects the symmetry class of patterns. For convenience (and brevity for inclusion in the results table), each symmetry class is described by a single letter that embodies. This can be one of:

• . (none) is for asymmetrical patterns.
• - (orthogonal reflection) is for patterns with D1 symmetry, that are unchanged when reflected in a horizontal or vertical mirror (| or –).
• / (diagonal reflection) is for patterns with D1 symmetry, that are unchanged when reflected in a diagonal mirror (/ or \).
• ~ (180° rotation) is for stationary patterns with C2 symmetry, that are unchanged when rotated 180 degrees about a point.
• + (two orthogonal reflections) is for stationary patterns with D2 symmetry, that are unchanged when reflected in either horizontal or vertical mirrors.
• x (two diagonal reflections) is for stationary patterns with D2 symmetry, that are unchanged when reflected in either kind of diagonal mirror.
• @ (90° rotation) is for stationary patterns with C4 symmetry, that are unchanged when rotated 90 degrees about a point.
• * (8-way symmetry) is for stationary patterns that possess with eight-way D4 symmetry, that are unchanged when reflected in any kind of mirror, or rotated 90 or 180 degrees.

This selects the glide symmetry class of periodic patterns that may reform rotated or reflected multiple times during their periods. The same notation is used as for symmetry:

• . (none) is for patterns without glide symmetry. Modulus is the same as period. This can apply to patterns with any kind of symmetry.
• – (orthogonal reflection) is for patterns with D1 glide symmetry, that reflect themselves horizontally or vertically. Modulus is period/2. This can apply to asymmetrical patterns or patterns with orthogonal reflection or 180° rotation symmetry.
• / (diagonal reflection) is for patterns with D1 glide symmetry, that reflect themselves diagonally. Modulus is period/2. This can apply to asymmetrical patterns or patterns with diagonal reflection symmetry. (For patterns with 180° rotation symmetry, this is equivalent to T.)
• ~ (180° rotation) is for stationary patterns with C2 glide symmetry, that rotate themselves 180 degrees about a point. Modulus is period/2. This can apply to asymmetrical patterns. (For patterns with reflection symmetry, this is equivalent to their symmetry.)
• @ (90° rotation) is for stationary patterns with D4 glide symmetry, that are rotate themselves 180 degrees about a point. This can apply to asymmetrical patterns, in which case modulus is period/4. It can also apply to patterns with 180 degree reflection symmetry, in which case modulus is period/2.

This selects a sub-class of oscillator or spaceship:

• Any matches everything.
• Phoenix matches patterns that have no cells that survive in any generation (i.e. for oscillators, there are no stator cells).

This selects a sub-class of oscillator:

• Any matches everything.
• Flip-flop matches patterns whose rotor cells die only from under-population.
• On-off matches patterns whose rotor cells die only from over-population.

This selects a sub-class of oscillator:

• Any matches everything.
• Babbling brook matches oscillators whose rotor consists entirely of an open chain of two or more cells, each with exactly two rotor neighbors, except the end cells that have only one neighbor each (e.g. beacon, test-tube baby).
• Muttering moat matches oscillators whose rotor consists entirely of a closed chain of two or more cells, each with exactly two rotor neighbors (e.g. blinker, clock, bipole).

This is where you enter the pattern to match. You can enter the pattern in one of two ways:

• As an image of dead and living cells. This is typically done with . and o characters, but all punctuation and line-drawing characters are treated as dead cells (. , : ; - | +) and all others are treated as living cells. Comment lines at the start beginning with # or ! are ignored. The pattern cannot include any ! characters.
• A text life file exported from another program like Golly. Formats currently supported are RLE, Cells, Life 1.05, and Life 1.06. The format is fairly forgiving (for example, comments can begin with # or ! regardless of format; RLE files can omit the header line or trailing ! character, although one or the other must be to identify this as RLE format.)
• Results from the Paste button are also displayed here.

Cells entered as ? are treated as wildcards, and match both living and dead cells. These are useful when searching for parts of patterns.

This selects how search results are displayed:

• List displays the results in a text table, with each row indicating one matched pattern. The pattern's name(s), period, population, and number of gliders required to synthesize it are displayed. Additional columns may also be present if other properties are used as search constraints, or as sort order.
• Stamp page displays the results as a stamp page image, in the same format as other pages on this site. Each matched pattern's image is displayed, as well as the number of gliders required to synthesize it. Rarity may also be displayed if frequency or rarity is used as a search constraint or sort order. Typically up to 110 patterns can be displayed on each page, although this number may be smaller if any larger patterns occur in the search result list.

If this is checked, tool tips are displayed whenever you hover your mouse for several seconds over any control, input field, or displayed results. If you find tool tips unnecessary or annoying, uncheck this.

This selects how numbers should be displayed:

• Real displays numbers with decimal places, e.g. 1.25. Very large and very small numbers are displayed in scientific notation, e.g. 1.25e10.
• Rational displays numbers as fractions, e.g. 5/4.
• Integers are always just displayed as integers, e.g. 42.
• Numbers too large to display in the result list view are always shown in scientific notation.

This selects the maximum number of results to show in the search result table.

This is not used in the stamp page view, where the number of displayed results depends on the size of the patterns displayed.

This selects the order in which search results are displayed. This selects the primary sorting order. If multiple patterns have the same value, they are then sorted by period, population, and then name.

In the stamp page view, the secondary sorting order is by period, population, and then pattern image, as in the rest of this site.

Press this button to begin a new search, based on the criteria entered in the table above.

Press this button to reset all fields in the above form to their initial values.

Press this button to paste the pattern image at the bottom of this page into the above text box in human-readable text format.

This selects the format of data pasted by the Paste button:

• RLE displays the pattern in RLE format. This consists of an optional comment block, a header line, and the pattern stored in run-length encoded text format, which is ideal for copying to modern programs like Golly, and for text interchange, e.g. email. Most pattern files on this site are in RLE format. This is ideal for moderate to large patterns with dimensions up to around 1000x1000 (and is much more compact than plain text for such patterns), but becomes unwieldy for huge patterns like Gemini and Caterpillar, with populations in the millions.
• Cells displays the pattern in human-readable format, as an array of . (dead) and O (living) cells. It may be preceded by a block of comments beginning with ! characters.
• Life 1.05 displays the pattern in the format used by the Life 1.05 program. It consists of a header comment block, followed by the pattern stored in plain text as an array of . (dead) and * (living) cells.
• Life 1.06 displays the pattern in the format used by the Life 1.06 program. It consists of a header comment block, followed by the pattern stored as a set of coordinate points for each living cell, one per line. While this can be more compact than plain text, it is less compact than RLE,

Press this button to open the search help page in another window.

Enter the expression to be evaluated here.

Press this button to evaluate the JavaScript expression on the left and display the results in the text box above.

This indicates the status of the search, and when the search is completed, how many results were found, if any.

Press this button to select the first page of multiple-page results.

Press this button to select the previous page of multiple-page results.

Press this button to select the next page of multiple-page results.

Press this button to select the last page of multiple-page results.

This shows which page is displayed from multiple-page results. You can jump to a particular page by entering its number.

This shows which page is displayed from multiple-page results. You can jump to a particular page by selecting its number.

This is the stamp page of results of the search. Clicking on it has the following effects:

• Clicking on a pattern's image selects that pattern, and displays its properties in the table below.
• Clicking on the top left corner of the stamp page scrolls to the previous page, if multiple pages are available. This is the same as the < button.
• Clicking on the bottom left corner of the stamp page scrolls to the next page, if multiple pages are available. This is the same as the > button.
• Clicking on the bottom right corner of the stamp page selects the entire stamp page as a single pattern. This is useful for pasting it as a whole into another program.

This is the list of results of the search. Clicking on it has the following effects:

• Clicking on one of the column headers selects that property as the primary sort order, displays it in green, and sorts by that property in ascending order. Clicking on the same column again displays it in red and sorts in reverse order. This is the same as the "Sort results by" selection box.
• Clicking on a pattern name selects that pattern, and displays its properties in the table below.

This shows the cellular automata rule for the pattern being displayed:

• Life is Conway's Game of Life, the default rule.
• B2/S2 is an extremely explosive rule.
• B34/S34 is an interesting rule, once considered a viable alternative to Life, but that has since been determined to be too explosive to be very useful.
• Niemiec's rule 1 is a rule that features several natural spaceships that move at different velocities and directions.
• Niemiec's rule 0 is a less interesting rule, but it includes two additional unusual spaceships.
• Other rules may appear here when searching for an RLE file from a rule that is not supported by this site. This can only appear for patterns being searched, as such patterns can never be found.
• Unknown is shown when an image search doesn't specify a rule, and doesn't yield any results.

Click on the rule name to open up the page for that specific rule.

Click on "Rule" to open up the page for selecting rules.

This shows the pattern's name (or multiple names separated by semicolons, if the pattern has more than one).

Click on the name(s) to open up synthesis file for the pattern.

Click on "Names(s)" to open up the page for selecting patterns by name.

This only appears for patterns that have multiple synthesis files. This can happen in one of three circumstances:

• Some very large (or difficult to synthesize) objects may have multiple syntheses separated into different files.
• Many methuselahs that produce large results, especially those that release multiple gliders, have one file showing multiple syntheses, and another containing only one image, that allows the methuselah to be run to completion without multiple copies interfering with each other.
• Finally, some patterns have additional properties that are best illustrated in a separate file (e.g. the Queen bee's ability to eat gliders in many different ways).

Click on "Run methuselah" or "View alternate synthesis" to open up the alternate synthesis file for the pattern.

This only appears for patterns that have syntheses in multi-color Life.

Click on "View multi-color synthesis" to open up multi-color synthesis file for the pattern.

Click on "Multi-color" to open up the page for all multi-color syntheses.

This shows a pattern's population in its minimum phase. If the population has a different maximum or average population, these are also shown in parentheses.

Click on the population to open up the page for that population, focused on the sub-category where the pattern is listed.

Click on "Population" to open up the page for selecting patterns by size.

For still-lifes from 16 to 17 bits, if this object was on the list of difficult-to-synthesize ones that were the last for which syntheses were developed, click on "Difficult objects" to see it within the context of that list.

This shows a pattern's smallest bounding box. "Smallest" is determined in terms of area (or, when areas are the same, by perimiter). In parentheses is shown the "squareness" of this box (i.e. ratio of height to width). This is 1 for square patterns, and smaller for rectangular ones.

This shows a pattern's largest bounding box. "Largest" is determined in terms of area (or, when areas are the same, by perimiter). In parentheses is shown the "squareness" of this box (i.e. ratio of height to width). This is 1 for square patterns, and smaller for rectangular ones. This can be 0 for patterns that expand infinitely in one dimension. It is defined properly for patterns that expand infinitely in two dimensions, because they may expand at different rates (for example, the B heptomino releases two gliders escaping at right angles, expanding twice as fast in their common direction, so its ratio is ½.)

This shows the symmetry class of patterns. For convenience (and brevity for inclusion in the results table), each symmetry class is described by a single letter that embodies. This can be one of:

• . (none) is for asymmetrical patterns.
• – (orthogonal reflection) is for patterns with D1 symmetry, that are unchanged when reflected in a horizontal or vertical mirror (| or –).
• / (diagonal reflection) is for patterns with D1 symmetry, that are unchanged when reflected in a diagonal mirror (/ or \).
• ~ (180° rotation) is for stationary patterns with C2 symmetry, that are unchanged when rotated 180 degrees about a point.
• + (two orthogonal reflections) is for stationary patterns with D2 symmetry, that are unchanged when reflected in either horizontal or vertical mirrors.
• x (two diagonal reflections) is for stationary patterns with D2 symmetry, that are unchanged when reflected in either kind of diagonal mirror.
• @ (90° rotation) is for stationary patterns with C4 symmetry, that are unchanged when rotated 90 degrees about a point.
• * (8-way symmetry) is for stationary patterns that possess with eight-way symmetry, that are unchanged when reflected in any kind of mirror, or rotated 90 or 180 degrees.

If the pattern has glide symmetry, its glide symmetry class is also shown. It uses the same notation as used for symmetry:

• – (orthogonal reflection) is for patterns with D1 glide symmetry, that reflect themselves horizontally or vertically. Modulus is period/2. This can apply to asymmetrical patterns or patterns with orthogonal reflection or 180° rotation symmetry.
• / (diagonal reflection) is for patterns with D1 glide symmetry, that reflect themselves diagonally. Modulus is period/2. This can apply to asymmetrical patterns or patterns with diagonal reflection symmetry. (For patterns with 180° rotation symmetry, this is equivalent to T.)
• ~ (180° rotation) is for stationary patterns with C2 glide symmetry, that rotate themselves 180 degrees about a point. Modulus is period/2. This can apply to asymmetrical patterns. (For patterns with reflection symmetry, this is equivalent to their symmetry.)
• @ (90° rotation) is for stationary patterns with C4 glide symmetry, that are rotate themselves 180 degrees about a point. This can apply to asymmetrical patterns, in which case modulus is period/4. It can also apply to patterns with 180 degree reflection symmetry, in which case modulus is period/2.

This shows the object category of the pattern, along with its sub-category (which is typically based on its population):

• Still-life describes objects that repeat, and have a period of 1, i.e. no births and deaths.
• Pseudo-still-life describes pseudo-objects that repeat, and have a period of 1.
• Oscillator describes objects that repeat, and have a period of more than 1.
• Pseudo-oscillator describes pseudo-objects that repeat, and have a period of more than 1.
• Spaceship describes objects that repeat, but are translated in space when they do so. This also includes pseudo-spaceships (pseudo-objects that behave similarly), and flotillae (two or more traveling in tandem). Some flotillae form large categories that have special names (e.g. A-draggers, hive-nudgers, etc.)
• Wick stretcher describes wick stretchers: spaceships that leave output behind them that consists of an fixed number of ever-growing objects, and constantly increase in population.
• Puffer describes puffer trains: spaceships that leave output behind them that consists of an ever-increasing number of objects, and constantly increase in population.
• Gun describes spaceship guns: oscillators that produce spaceships that escape, and constantly increase in population.
• Breeder describes breeders: patterns whose population increases quadratically with time.
• Constellation describes collections of two or more stable, oscillating, and/or moving objects and/or pseudo-objects.
• Methuselah describes small patterns that are not stable, but that run for a long time before stabilizing.
• Not quite stable pattern describes patterns that aren't quite stable, but that closely objects that are. These are always listed here, rather than under the categories they resemble.

Click on the category name to open up the page for that specific category, focused on the sub-category where the pattern is listed.

Click on "Category" to open up the page for selecting patterns by category.

This describes the number of gliders needed to synthesize an object. It can be a number, or one of these:

• Known describes patterns for which it has been shown that they can definitely be synthesized, but for which no synthesis has yet been attempted. This can currently includes 15- and 16-bit still-lifes, 17-bit pseudo-still-lifes, and period-2 pseudo-oscillators from 17 to 19 bits.
• x describes patterns for which no synthesis is yet known.
• x+number describes patterns for which a partial synthesis exists, based on a predecessor that does not yet have a synthesis.
• TBD describes patterns for which no synthesis has yet been attempted. It is not known whether syntheses exist using currently known techniques.

In addition, the relative number of gliders may be noted in parentheses if it is equal to or greater than the population.

Click on the number to open up the page for that specific number of gliders, if it is available. (This is only available for Life, and is provided for 2-6 gliders for all objects, and Unknown, Partial, and =1 and >1 gliders per bit for selected objects.)

Click on "Gliders" to open up the page for selecting patterns by cost in gliders.

This describes the heat of a pattern. This is defined as the average number of unstable cells in each generation. This is zero for still-lifes and pseudo-still-lifes. It can be infinite for infinitely-expanding patterns, such as guns, and puffers that leave non-still objects. It is unknown for a few large spaceships. For methuselahs, this is the heat of the final census

This describes the period of a pattern. This is the number of generations it takes to return to its original state (possibly translated). For patterns with multiple components, this is the GCD of all components taken together. For infinitely expanding patterns, this includes both the generator (i.e. gun or puffer) and the resulting output. This can be infinite for patterns that expand infinitely in an irregular fashion.

If it differs from the period, the modulus is shown in parentheses. This is the number of generations that it takes for the pattern to return to its original state, regardless of rotation or reflection. This is the period for most patterns, but can also be period/2 for patterns with glide symmetry, or even period/4 for asymmetrical patterns that rotate 90 degrees four times each period.

This describes the frequency and rarity of a still-life or oscillator. Frequency is always a large real number for the 152 measured objects, while rarity (its inverse) is a large real number. It is not shown for other objects (for which it is Unknown), or for other object categories (for which it is N/A).

Click on the number to open up the page for that specific category of objects sorted by rarity.

Click on "Frequency" to open up the page for viewing all naturally-occurring objects in order of frequency.

This describes the T.T.S. (time to stabilize) of a pattern. It is zero for all periodic patterns, and non-zero for methuselahs. It is infinite for patterns that expand without limit without ever reaching periodicity. The E.F. (evolutionary factor) is also shown in parentheses; this is the T.T.S. divided by the initial population.

This describes the temperature of a pattern. This is defined as the heat divided by the population, or total number of unstable cells in all generations, divided by the total populations of all generations. This is a similar measure to heat, but scales with population, so it is possible to define it meaningfully even for infinitely-expanding patterns. (This is similar to the corresponding measures from physics; doubling the size of an object doubles its heat, but does not alter its temperature).

This describes the velocity of a moving pattern, e.g. how far it moves in each period, divided by the period. This is zero for most pattern categories, and is not shown for those, and a non-zero number between 0 and c for spaceships and puffers. It is shown as a direction and a rational multiple of c. In most rules, this cannot exceed c/2 for orthogonal movement (although it can reach c in B2/S2). In most rules, this cannot exceed c/3 for diagonal movement (and it cannot exceed c/4 in Life).

The direction can be one of:

• Orthogonal for patterns for which movement in in one axis only.
• Diagonal for patterns for which movement is by the same same amount in both axes.
• Oblique for other patterns, i.e. those that move in both axes, but a different amount in each. These are extremely rare.

This describes the volatility of the pattern. This is defined as the number of rotor cells divided by the number of rotor plus stator cells. This is zero for still-lifes and pseudo-still-lifes. It is a non-zero number between 0 and 1 for for oscillators and pseudo-oscillators. It is always 1 for spaceships. For infinitely-expanding patterns, this value is dominated by that of the expanding output. For methuselahs, this is the volatility of the final census.

This also describes the strict volatility of the pattern in parentheses, if it differs from the volatility. This is similar to volatility, but only considers the cells that oscillate at the full oscillator or spaceship period, rather than all rotor cells. It is defined as the number of full-period cells divided by the number of rotor plus stator cells. This is equal to volatility for still-lifes and pseudo-still-lifes (for which it is also zero), for all oscillators and spaceships with prime periods, and for totally volatile oscillators of other periods.

If strict volatility is shown, the ratio of strict volatility and volatility is also shown. This always varies between 0 and 1.

This is the image of the selected pattern.

Click on the image to open up synthesis file for the pattern. (This is only available for patterns found as the result of a search.)