Zendo is a game of inductive logic by Kory Heath where one player — the "master" — creates a secret rule and the other players — the students — propose new "koans" and make guesses in order to discover the master's rule ("become enlightened").

Want *real* koans?

Rules of the Game

In the original game of Zendo, koans are configurations of stackable pyramids that come in several sizes and colors. These pieces are known as Looney Pyramids or Icehouse pieces.

Zendo need not use pyramids exclusively. Another popular variant is Text Zendo, where koans are comprised of words instead of pyramids. Text Zendo is the default format for Zendo challenges on SDG. Number Zendo and Image Zendo are available as variants. Using just these three "mediums" for Zendo, quite a few variations have been invented and used by SDG players.

The same basic rules as the Icehouse Zendo game are used for nearly all Zendo variants, so refer to the link above to learn the game. Guidelines and notes specific to each variation are given below.

Image Zendo

Image Zendo on SDG is usually used for pyramid Zendo, but any images may be used. The master will tell you what makes a koan allowable in the dojo. Note that SDG resizes all images to 200x200 pixels as this may place limitations on what is possible to represent.

Pyramid Zendo

Example koan for Pyramid Zendo

Pyramid Zendo is played either with photographs of actual pyramids or with 3-D images of pyramids rendered with the POV-Ray 3-D raytracing program. See a sample game.

SDG maintains a searchable library of pyramid koan images with more than 100,000 entries! You will often be able to find the koan that you need already in the library. If you do need to create a new koan, use the SDG POV-Ray Playground. The following resources are all accessible from the Services link on the main SDG site:

Guidelines for Play

  • The only valid attributes are the observable ones, but generally you are observing an image of a pyramid koan. The image is not the koan. The image is a picture of the true koan, and the master must honestly answer questions of fact regarding the true koan. ("Are those two pieces actually touching?" "What colors and sizes are found in this koan?")
  • Masters should inform students if the image itself is the koan, so that features such as a pyramid going out of frame, reflecting or transmitting light from another pyramid, casting a shadow on another pyramid, or pointing right or left, are known to be observable.

Pixel Zendo

Example koan for Pixel Zendo

Pixel Zendo is a recent variation invented by SDG user mathgrant and uses images of rectangular grids of colored squares or "pixels". In the games played so far, allowable koans have been of any size (as long as the grid is rectangular) and pixels are usually only black or white with some other color (typically red) used to separate the pixels. There is no reason though that a master could not choose to limit the size or allow additional pixel colors for a particular game. See a sample game.

See the page on Making Pixel Koans for software suggestions, tips, and templates that make it easy to create Pixel Zendo koans.

The following terminology has been suggested by mathgrant and adopted by other players of Pixel Zendo.

  • Coordinates: The coordinates of a pixel are (x,y), where x and y are non-negative integers. The x-coordinate, the first number, represents what column the pixel is in, with the leftmost column being 0. The y-coordinate, the second number, represents what row the pixel is in, with the topmost row being 0. The pixel in the upper-left corner, with coordinates (0,0), can be called the origin.
  • Adjacency: For the sake of clarity, do not use the word "adjacent" by itself. Instead, use "orthogonally adjacent", "diagonally adjacent", or "near". Two pixels are near each other if they are orthogonally or diagonally adjacent.
  • Color groups: A color group is a group of pixels of the same color which all form a single polyomino (that is, it's possible to get from any pixel in the group to any other pixel by moving orthogonally one pixel at a time). A white group is a group of white pixels; a black group is a group of black pixels. A group is bounded if it is not orthogonally adjacent to another pixel of the same color. The size of a group is how many pixels the group has.
  • Distance: The horizontal distance, or x-distance, between two pixels is the difference between their x-coordinates. The vertical distance, or y-distance, between two pixels is the difference between their y-coordinates. The taxicab distance between two pixels is the sum of the x- and y-distances. The Euclidean distance between two pixels is the square root of the sum of the squares of the x- and y-distances (think Pythagorean theorem). Example: for the pixels at (0,0) and (4,3), the x-distance is 4, the y-distance is 3, the taxicab distance is 4+3=7, and the Euclidean distance is sqrt(4^2+3^2)=5.

Shape Zendo

SDG user AnalogKid has suggested that images composed of lines, circles, squares, or any other 2-D shapes in various colors and sizes would be a viable alternative to the 3-D pyramid images for playing Zendo on SDG. No one has yet tried running such a game.

Text Zendo

Text Zendo is typically played with koans being either a single word, a sequence of words, or arbitrary text. But a huge number of specialized variations are possible within Text Zendo and some masters have experimented quite liberally. A few possible variations that have been used are given after the basic rules for "Word Zendo".

Word Zendo

  • Only observable attributes of the words are valid. Language, meaning, and pronunciation are not relevant, since they can't be observed in the dojo.
  • There is no reason foreign languages or even gibberish can't be used as koans. The Master will tell you what's allowed to be a koan.
  • In cases of foreign languages, accents are usually ignored.
  • Capitalization and punctuation are usually ignored.
  • Whitespace is often ignored except in that it separates one word from the next.
  • Vowels are usually AEIOU.
  • The order of letters in the alphabet may be important. That is, in terms of the Spock rule, Spock is assumed to know the order of the alphabet.
  • Koans should usually consist of no more than 5 words as excessive length can over-cloud the rule.
  • Some masters have tried dojos in which the meaning of words is an observable attribute, but this is more nebulous than is desirable for Zendo. Not everybody agrees about the meanings of even everyday words
  • Some masters have limited the possible koans to specific categories such the names of actors & actresses or to band names, etc.
  • If the master is using a dictionary or other reference work (Wikipedia, say, or Google) to determine the Buddha nature, the master must disclose this to the students.

Playing Card Zendo

SDG user Zotmeister has invented a variant where koans are combinations of standard playing cards. Cards are represented in the dojo by letters corresponding to their rank (AKQJT98765432) followed by their suit (SHDC). In one game, koans were ordered pairs of cards written "X on Y" (eg. "2H on 2C"). In another game, koans were unordered sets of four distinct cards (eg. 2C, 5C, 8D, JD). Many other koan formats for Playing Card Zendo are possible and, indeed, this variant suggests that Text Zendo on SDG can be used to play Zendo with any sort of collection of real or imagined objects, as long as a clear notation for the koans can be articulated. (see Musical Zendo below).

Meta Zendo

In Meta Zendo (invented by SDG user GregF ?), koans are Zendo rules for one of the other types of Zendo and the Master's rule is a "metarule" that describes which Zendo rules have the Buddha nature. If that sounds convoluted, consider these examples from a sample game here on SDG in which koans were valid rules for single-word Text Zendo.

The Master's metarule was AKHTBN iff it would mark "zendo" white.

HAS koans included:

  • AKHTBN iff it contains at least three different consonants. (Y and w are always consonants)
  • AKHTBN iff the first consonant is not repeated anywhere else in the koan.

HAS NOT koans included:

  • AKHTBN if the koan contains at least 7 letters.
  • AKHTBN iff the 3rd letter is an E.

To get a better sense of the possibilities for Meta Zendo, see the rule and the discussion in another sample game.

Programming Meta Zendo

A more formal version of regular meta zendo. Koans are functions in some programming language that return a boolean value.

Cypher Zendo

In Cypher Zendo, the Master chooses a simple substitution cypher (a "secret code") that replaces each letter of the alphabet by another particular letter such that no two letters are replaced by the same letter. Koans are strings of letters and they have the Buddha nature iff the cypher transforms them into a valid word. Students are trying to guess the master's cypher (i.e. break the secret code). The Master and students use an online dictionary as a reference for which words are considered valid. For complete rules and examples, see the Cypher Zendo page. See a sample game.

Musical Zendo

SDG user AnalogKid thinks that using musical melodies or chords as koans could be fun. Koans could be represented on SDG using a textual notation indicating pitch and rhythm (something like "4/4 - 4: C4 C4 G4 G4 | A4 A4 2: G4 | 4: F4 F4 E4 E4 | D4 D4 2: C4" for Twinkle, Twinkle, Little Star). Many different properties could be used to form rules: pitches, intervals, scales, key, durations, meter, etc.

Number Zendo

In Number Zendo, koans are usually a single number. Many Number Zendo dojos use only integers, and often only positive integers. Some have used "decimals" (real numbers with a terminating decimal representation), ANY real number (including repeating fractions or irrational numbers), complex numbers, or pairs of numbers (planar coordinates). SDG user Jesse even ran a game where koans were single-variable functions! (albeit in a Text Zendo dojo). The Master will tell you what makes a valid koan.

Rules might consider

In other words, some require math, others won't.

Here are some examples of things to consider when playing Number Zendo:

Rules in the Game (The Buddha Nature)

  • See the Zendo page on the Icehouse games fan site for a glossary of Zendo terminology. This is helpful when considering the rules that are possible.
  • Past Zendo rules used in SDG games are archived and can be good for getting ideas.
  • The Zendomizer can help you make some interesting Icehouse Zendo rules.
  • Bongard Problems are a good solitaire alternative to Zendo.

SDG Implementation Details

Text Zendo is the default format for Zendo challenges on SDG.Number Zendo and Image Zendo are available as variants.

  • The user who issues the challenge will be the master. Players who are new to Zendo should play a few games first before issuing a challenge.
  • SDG Zendo supports 2-5 students.
  • Number Zendo koans may contain non-numerical characters (if the master allows). The primary difference from Text Zendo appears to be that the koans are sorted numerically.
  • Image zendo koans have an optional annotation, which most browsers show when the mouse pointer hovers over the image.
  • Only the master can change the pop-up text of a koan in the dojo, by clicking on the koan label; but a student can submit an annotation when submitting a koan. That description lets a student submit an ambiguous image but choose to specify either "touching" or "very close but not touching", for example.
  • Students in the dojo may click on the koan label to reach the koan tagging page. Any number of tags may be defined by the student and applied to any koans in the dojo; the student may subsequently filter out koans according to tags. Tags are like notes, private, so nobody else can see that you're interested in which koans have exactly two orange pieces.
  • Masters may click on the koan label to change the koan's properties (including re-marking it) or to delete a koan entirely.
  • Set Guess Mode allows the Master to force the game to skip to the guessing phase of a player's turn (skipping entering a new koan). This can be useful if the Master needs to rotate back around to a player's turn after they have already submitted a koan.
  • One oddity of the implementation is that at the beginning of the game, when the Master adds and marks the first two koans, the game will skip the first two players turns but also send out notifications that it is their turn. This also happens if the Master adds koans later in the game that are not directly in reply to an incorrect guess.
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