Operator arity at every depth

These are counts in one KanjiVG snapshot. A count is not a rule of stroke order. The page makes no claim about meaning.

Cinnabar is the first argument. Indigo is the second. Ochre is the third. The plate plays the character’s own stroke order. Click a plate to replay. With reduced motion the finished character stays still, and the colors stay. The draw timings are unchanged. The plate stays cream in either theme.

First argument
Second argument
Third argument

How a node is read

Question: Across the 2,136 jōyō files, how many composition nodes are two-place, three-place, or four-or-more, at depth 1, depth 2, and depth 3 or below, and for each operator? Of the three-place nodes that have an operator, and of the nested binaries that cover the same row or column, how many are hits under the depth-first walk with the exception-page rules on?
Composition: A group whose slots_of arity is at least 2. These are the 6,176 composition nodes on Operator trees. Depth 1 is the character group. Each step into a child group adds one. A character whose root is not a composition is counted with the characters, and it is not a node.
Arity: The number of slots: two-place, three-place, or four or more. Four or more slots have no IDC in the box reading.
Depth: Depth 1 is the character group. Depth 2 is a composition inside it. Depth 3+ is every composition at depth 3 or below.
Operator: The kvg:position row when that row exists, otherwise the bounding-box operator. A box reading is starred. A composition with no operator is counted on its own row.
Flat three-place: A composition of arity 3 that has an operator. The three-argument operators in the position rows and in the box reading are ⿲ and ⿳. ⿲ is a row. ⿳ is a column. A three-place node with no operator is counted beside them.
Nested binary: A ⿰ or ⿱ whose one argument is itself that same operator, with exactly two arguments of its own, and neither of those is again that operator. The three leaves are a row, or a column. ⿰(a, ⿰(b,c)) nests the second argument. ⿱(⿱(a,b), c) nests the first. A chain of four leaves counts the inner triple. These nodes are two-place.
Walk: The depth-first walk on Evaluation rules for the exception classes, with that page’s three rules on. A hit emits the subtree’s strokes in file order. Otherwise the class is inside-first, frame-last, part-split, walk-miss, or unmapped. An unmapped subtree stays unmapped.
Classes: Hit, inside-first, frame-last, part-split, walk-miss, and unmapped. On a depth-1 composition the class is the character class. The six character classes on the exception page are the depth-1 node classes plus the characters whose root is not a composition.

Arity at each depth

Arity by depth

Arity	Depth 1	Depth 2	Depth 3+	Nodes

Compositions at each exact depth. Depth 1 is the character group. The bars add to the composition nodes.

Exact depth

Depth	Nodes

Exact arity

Arity	Nodes

Each operator

Operator, arity, and depth

Operator	Reading	Two-place	Three-place	Four or more	Depth 1	Depth 2	Depth 3+	Nodes

Readings with no node

Operator	Reading	Nodes

Hits and exception classes

By arity

Arity	Nodes	Hit	Inside first	Frame last	Part split	Walk miss	Unmapped	Hit rate

By depth

Depth	Nodes	Hit	Inside first	Frame last	Part split	Walk miss	Unmapped	Hit rate

Flat three-place and nested binary

Eight patterns

Pattern	Nodes	Depth 1	Depth 2	Depth 3+	Position row	Starred	No operator

Hits among flat three-place nodes that have an operator, and hits among nested binaries. The two bars are two counts.

The same walk on both

Pattern	Nodes	Hit	Inside first	Frame last	Part split	Walk miss	Unmapped	Hit rate

Character classes

Depth-1 nodes and the other roots

Class	Depth-1 node	Not a composition	Character

Plates

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