Fold a tree with a binary operator f:

Start by applying an operator g to the data in the leaves:

Create a visualization of a tree:

Fold a tree with children specified as an association:

Fold a leaf:

Fold an inner node with no children:

Fold a tree with children:

Fold a tree with multiple levels:

Apply an operator to the leaves:

Fold a property of subtrees:

Fold a tree with children specified as an association:

Use the operator form of TreeFold on one argument:

Use the operator form of TreeFold on two arguments:

Get a nested list of the data in the leaves of a tree:

Construct a tree from the atoms of an expression:

Convert this tree to nested lists:

Total the data in the leaves of a tree:

Total the data in a tree:

Create a tree of terms in a linear recurrence:

Compute the terms of the linear recurrence:

Convert a tree to an XMLElement:

Convert a tree to JSON rules:

Convert a tree to a TextElement:

Compute the minimum level of leaves in a tree using TreeFold with this function:

Display a tree as a grid:

Get a list of US cities with populations over 100,000:

Construct a graph giving the hierarchical clustering of the cities according to their geodetic positions:

Convert the clustering hierarchy from a Graph object to a Tree object:

For each leaf, obtain the geodetic position of a city from its index in the hierarchical clustering graph:

For each subtree representing a cluster, give the tree containing the spatial median of its children:

Obtain a tree of geodetic positions by using the position of a city for each leaf and the spatial median of the positions for each cluster:

Show the edges in this tree of geodetic positions on a map of the United States:

Create a family tree:

Create an association giving the dates of birth:

Define a function that compares two people, giving the person who was younger when they had their first child, together with that child and their age when that child was born:

Define a function that compares two siblings, giving the older sibling together with their date of birth, in addition to the youngest first-time parent among their descendants:

Define a function that gives the youngest first-time parent among a person's descendants, given the results for their children:

Find the youngest first-time parent in the tree, together with their first child and their age when the child was born:

Fold gives the result of successively applying a binary operator f to the elements of a list:

TreeFold gives the result of successively applying a binary operator f to the data of a tree:

TreeFold applies the operator f to the list of results for each child:

TreeFold[f,Tree[data,None]] gives data:

TreeFold[{f,f_-1},Tree[data,None]] applies the operator f_-1 to data instead:

TreeFold[f,Tree[data,{…}]] gives f[data,{…}]:

This is true even if the tree has no children:

TreeFold[f,tree,h] gives the result of applying f to both h[tree] and the list of results TreeFold[f,tree_i,h] for the children tree_i:

TreeFold[f,tree] is equivalent to TreeFold[{f,Identity},tree]:

TreeFold[{Tree,Tree[#,None]&},tree] is equivalent to tree:

TreeFold applies a function to the data and results for the children:

TreeMap can compute the same result:

The new data of the root is the result of TreeFold:

Construct a tree from the heads in an expression:

Use TreeFold to insert a parent node above each subtree:

This corresponds to mapping on the arguments in an expression:

Map maps on the arguments in an expression by default:

Construct a tree from the atoms in an expression:

Use TreeFold to insert a sibling node before each subtree:

This corresponds to mapping on the subexpressions in an expression:

Map maps on the subexpressions in an expression with HeadsTrue:

TreeFold[{f,f_-1},tree] is equivalent to TreeFold[f,TreeMap[f_-1,tree,{-1}]]:

First map the operator f_-1 on the leaves of the tree:

Then fold the tree using the operator f for internal subtrees:

TreeFold can be used to compute the depth of a tree:

TreeFold can be used to compute the size of a tree:

TreeFold can be used to convert a tree to nested rules:

TreeFold can be used to create an expression from the leaves of a tree:

Construct a tree with levels giving the triangles in the 0- through 3-step Sierpiński triangles:

Obtain the 3-step Sierpiński triangle from this tree:

Construct a tree with levels giving the intervals in the 0- through 3-step Cantor sets:

Obtain the 3-step Cantor set from this tree: