Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 NestTreeInteractive

Source Notebook

Interactively construct a tree

Contributed by: Ian Ford

ResourceFunction["NestTreeInteractive"][f,expr0]

gives an interactive tree with initial data expr0, where clicking a leaf with data expr adds new children defined by f[expr].

ResourceFunction["NestTreeInteractive"][f,expr0,h]

additionally applies h to the data of the clicked node.

Details

ResourceFunction["NestTreeInteractive"] is an interactive version of NestTree.
ResourceFunction["NestTreeInteractive"] grows Tree objects, adding successively deeper levels of children to the leaves using an operation f.
ResourceFunction["NestTreeInteractive"] is useful for constructing a tree from an expression.
Whenever a leaf Tree[expr,None] is clicked, it is replaced by Tree[expr,{Tree[expr1,None],…}], where f[expr] gives {expr1,expr2,…}.
If f returns None or {}, no futher levels can be added to that leaf.
In NestTree[f,expr,h], clicking a leaf Tree[expr,None] replaces it with Tree[h[expr],…].
f[expr] should give {expr1,expr2,…} or None.
If f does not return {…} or None, ResourceFunction["NestTreeInteractive"][f,expr,…] is equivalent to ResourceFunction["NestTreeInteractive"][List@*f,expr,…].

Examples

Basic Examples (2) 

Interactively build a tree from an expression:

In[1]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][Range[3 # - 1, 3 # + 1] &, 1]
Out[1]=

Clicking the leaf adds children:

In[2]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][Range[3 # - 1, 3 # + 1] &, 1]
Out[2]=

Children can be continually added by clicking the leaves:

In[3]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][Range[3 # - 1, 3 # + 1] &, 1]
Out[3]=

Give a function to apply to each new node:

In[4]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][Range[3 # - 1, 3 # + 1] &, 1, clicked]
Out[4]=

Applications (2) 

Interactively create a Calkin-Wilf tree:

In[5]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][ Replace[{m_, n_} :> {{m, m + n}, {m + n, n}}], {1, 1}, Replace[{m_, n_} :> m/n]]
Out[5]=

Interactively create a Stern-Brocot tree:

In[6]:=
ResourceFunction[ "NestTreeInteractive", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][ n |-> Replace[ ContinuedFraction[n], {as___, a_} :> Sort[FromContinuedFraction /@ {{as, a - 1, 2}, {as, a + 1}}]], 1]
Out[6]=

Requirements

Wolfram Language 13.0 (December 2021) or above

Version History

  • 1.0.2 – 04 March 2024
  • 1.0.1 – 19 January 2024
  • 1.0.0 – 12 January 2024

Source Metadata

Related Resources

Author Notes

Unlike NestTree, NestTreeInteractive does not support operations f that return <|…|> or Hold[…].

The output is reset when the notebook is closed, so to save the output, select the cell and choose the Cell ▶ Convert To ▶ Bitmap menu item.

License Information