Syntactically, there are three categories of statements: control-flow statements which contain sub-statements, statements which contain rules, and line statements. Additionally, declarations may occur where statements are expected.

When a block may have multiple children, these must occur either in an indented block after a colon ‘:’, or if there is only one child it may occur on the same line, after the colon.

Statements in MJr are said to “return true” or “return false”; this determines the program’s control flow. A statement typically “returns true” if it makes any changes to the current grid’s state.

A compilation unit is treated like a ‘sequence’ statement.

Control-flow statements

‘Markov’ statements

A markov statement executes its children in order of priority, returning back to the first child each time any child statement “returns true”. The markov statement itself “returns true” if any of its children did.


‘Sequence’ statements

A sequence statement executes each child repeatedly until it “returns false”, then moves onto the next child. The sequence statement itself “returns true” if any of its children did.


‘Limit’ statements

A @limit modifier is followed by an expression, which must be a runtime constant of type int, and then a sub-statement on the next line. The value of the expression determines the initial value of a “limit counter” which is initialised each time the parent block is entered, and counts down each time the modified statement “returns true”. Once the counter reaches zero, the limit statement “returns false” without executing its sub-statement.

A compilation error occurs if the sub-statement is another limit statement, a once statement, or a kind of statement which always “returns false”.

@limit Expression

Statements with rules

‘One’ and ‘Once’ statements

A one statement has a set of rewrite rules, and pseudorandomly chooses an applicable match of one of them. If an applicable match exists, that rewrite is applied to the grid and the statement “returns true”; otherwise it “returns false”.

one {Arguments}:

As a shorthand syntax, the keyword once may be written instead of one; this is equivalent to a one statement with a limit of 1. A once statement has no arguments.


‘All’ statements

An all statement has a set of rewrite rules, and applies rewrites in parallel. If any applicable matches exist, then a maximal subset of them is pseudorandomly chosen such that output patterns do not overlap, the rules are applied on these matches, and the statement “returns true”; otherwise, it returns “false”.

all {Arguments}:

‘Prl’ statements

A prl statement is similar to an all statement, except that overlapping output patterns are not prevented. If there are any applicable matches, then the rewrite rules are applied on every match in parallel, with any overlapping output patterns written in a pseudorandom order, and the statement “returns true”; otherwise, it “returns false”.

A prl statement has no arguments.


‘Convolution’ statements

A convolution statement applies a set of 1x1 rewrite rules to all matches in parallel, where the rules may make use of ‘sum’ expressions. There is one required argument, kernel, which determines the convolution kernel used by sum expressions within the statement. It must be a compile-time constant str equal to one of the following names:

Additionally, there is an optional argument, boundary, which must be a compile-time constant 1x1 pattern. If present, cells outside of the grid are treated as if they take values from the subset of the alphabet defined by boundary. A compilation error occurs if boundary is specified for a periodic grid.

The statement “returns true” if there were any applicable matches, otherwise it “returns false”.

convolution {Arguments}:

‘Map’ statements

A map statement has a set of rewrite rules whose input patterns are matched in an “input grid” and output patterns are written to a separate “output grid”. The input grid is the current grid, and the output grid is specified as an argument. The input and output grids may have different scales, in which case the input and output patterns of each rewrite rule must be scaled in the same proportion, and the position of the match in the input grid is scaled to the output grid in the same proportion.

A map statement always “returns false”, because it may make changes to outGrid but not the current grid. However, after a map statement executes, outGrid becomes the current grid.

A compilation error occurs if outGrid is the current grid.

map {outGrid=Expression}:

Line statements

‘ConvChain’ statements

A convchain statement runs the ConvChain algorithm to generate an image which is locally similar to a given sample pattern, by pseudorandomly replacing some grid cells. It has the following arguments:

The alphabet symbols present in sample form the “output set”.

On the first iteration of a convchain statement, a set of grid cells is initialised containing those cells which match the pattern on. Each cell in this set which does not already have a symbol in the output set is replaced with pseudorandom symbol from the output set. If any replacements were made, then the statement completes and “returns true”, otherwise it continues executing as below.

After initialisation, on each iteration the grid cells which originally matched on are pseudorandomly replaced with different symbols the output set, biased towards local similarity with sample. The statement “returns true” if any replacements were made, and “returns false” otherwise.

convchain {Arguments}

‘Log’ statements

A log statement logs a the value of an expression to the standard output stream (i.e. the console or terminal), and always “returns false”. The expression’s type must be one of bool, float, fraction, grid, int or str.

log Expression

‘Pass’ statements

A pass statement does nothing, and always “returns false”. It may be used as a placeholder in a block which is not yet written.


‘Path’ statements

path {Arguments}

‘Put’ statements

A put statement writes a pattern to the current grid at a given position, if it is not already present there. The position determines the top-left corner of where the pattern should be written. The pattern’s type must be an output pattern type.

A put statement always “returns false”, even when writing the pattern changes the grid. This is because even when a put statement is not idempotent, it is normally not intended to repeat.

put Expression at Expression

A put statement may have a condition, which must be an expression of type bool. If the condition is true, then the statement is executed as above; otherwise the pattern is not written.

put Expression at Expression if Expression

‘Use’ statements

A use statement changes the current grid to the value of an expression, which must be a compile-time constant of type grid. The context change persists beyond the current block. The statement always “returns false”.

use Expression

If the expression is a grid expression, then the keyword use may be omitted. This is a shorthand syntax, referred to as a “bare ‘use’ statement”.

grid [Alphabet]
grid {Arguments} [Alphabet]

In order to access the grid’s attributes (i.e. its width and height) or otherwise refer to the grid elsewhere, it is necessary to declare a variable holding a reference to the grid. This can be done with a declaration such as let g = grid ... followed by the statement use g, or with the following shorthand syntax, referred to as a use let statement:

use let Name = Expression

The use let statement is equivalent to the combination of a let declaration and a use statement; in particular, the variable is only in scope until the end of the current block, but the context change of the use statement persists beyond the current block.

Declaration statements

If a declaration occurs in a block of statements, then the declaration is in effect for the statements following it within that block.


Alternatively, the declaration may be followed by the keyword in, a colon ‘:’ and a block of child statements, in which case the declaration is in effect for the statements in that block.

Declaration in: