RandomTree
RandomTree[n]
gives a pseudorandom tree with n nodes.
RandomTree[n,k]
gives a list of k pseudorandom trees.
RandomTree[n,{k1,k2,…}]
gives a k1× k2×… array of trees.
RandomTree[{e1,…,en},…]
gives trees with nodes containing the expressions ei.
Details and Options
- RandomTree[n] samples from the discrete uniform distribution over the
labeled, rooted, ordered trees of size n, where 
is given by CatalanNumber[n-1]. Any reordering of the data or subtrees represents a different tree. » - RandomTree gives a different sequence of pseudorandom trees whenever you run the Wolfram Language. By using SeedRandom, you can get a repeatable sequence. »
- The data of the trees produced by RandomTree[n,…] is taken to be integers 1, …, n. »
- The data of the trees produced by RandomTree[{e1,…,en},…] is taken to be expressions e1, …, en. »
- RandomTree has the same options as Tree.
List of all options
Examples
open all close allBasic Examples (4)
Generate a random tree with 10 nodes:
RandomTree[10]Generate a list of random trees:
RandomTree[5, 3]Generate an array of random trees:
RandomTree[5, {2, 3}]Generate a tree of the lowercase letters a through z in the English alphabet:
RandomTree[Alphabet[]]Options (9)
Styling Individual Tree Elements (2)
Specify the label for the generated tree element:
RandomTree[3, TreeElementLabel -> "?"]Specify labels and styles for subtrees by position:
RandomTree[20,
TreeElementLabel -> {___, _ ? EvenQ} -> None, TreeElementStyle -> {___, _ ? OddQ} -> {LightRed, EdgeForm[{Red, Dashed}]}]Styling Entire Tree (4)
Specify labels and styles for all subtrees:
RandomTree[20, TreeElementLabel -> All -> None, TreeElementStyle -> All -> EdgeForm[Red]]RandomTree[20, BaseStyle -> LightRed]Specify the styles for both the edges and the edges of the tree elements:
RandomTree[20, BaseStyle -> {Dashed, EdgeForm[{Dashing[{}], Thick}]}]Specify the base style and styles for individual tree elements:
RandomTree[20, BaseStyle -> {Red, EdgeForm[None]}, TreeElementStyle -> All -> Opacity[0]]Tree Layout and Graphics Options (3)
Specify the orientation for the root:
RandomTree[10, TreeLayout -> Bottom]RandomTree[50, TreeLayout -> "RadialEmbedding", IconizedObject[«labels»]]Specify Graphics options:
RandomTree[50, Background -> LightBlue, ImageSize -> Full]Applications (1)
Properties & Relations (6)
RandomTree[n,…] uses integers 1, …, n:
RandomTree[7]RandomTree[{e1,…,en},…] uses expressions e1, …, en:
RandomTree[Characters["abcdefg"]]Use TreeMap to replace data in the tree:
TreeMap[Capitalize, %]RandomTree gives pseudorandom trees:
{RandomTree[6], RandomTree[6]}Use SeedRandom to get repeatable random trees:
{SeedRandom[1];RandomTree[6], SeedRandom[1];RandomTree[6]}Use BlockRandom to block one use of RandomTree from affecting others:
{BlockRandom[RandomTree[6]], RandomTree[6], RandomTree[6]}RandomTree[n] can produce n! CatalanNumber[n-1] different trees:
Table[n!CatalanNumber[n - 1], {n, 1, 8}]RandomTree[2, 20]//DeleteDuplicatesRandomTree[3, 200]//DeleteDuplicates//LengthRandomTree[4, 2000]//DeleteDuplicates//LengthRandomTree[5, 100000]//DeleteDuplicates//LengthRandomTree[n] samples from the uniform distribution over the labeled, rooted, ordered trees of size n:
RandomTree[3, 10000, IconizedObject[«image size»]]//Sort//TallyRandomTree generates random trees of a certain size:
SeedRandom[125];RandomTree[21]NestTree can be used to generate random trees with random data and numbers of children:
SeedRandom[3];NestTree[RandomInteger[10, RandomInteger[{1, 3}]]&, RandomInteger[10], 3]Text
Wolfram Research (2021), RandomTree, Wolfram Language function, https://reference.wolfram.com/language/ref/RandomTree.html (updated 2025).
CMS
Wolfram Language. 2021. "RandomTree." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/RandomTree.html.
APA
Wolfram Language. (2021). RandomTree. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RandomTree.html