Talk:H tree

Information visualization

Reference 5 to Nguyen, Quang Vinh; Huang, Mao Lin (2002). "A space-optimized tree visualization". IEEE Symposium on Information Visualization. pp. 85–92. doi:10.1109/INFVIS.2002.1173152 is wrong. The H-Tree is there part of the related work. It says that the H-Tree is not suitable for information visualization. The Wikipedia article implies the opposite. —Preceding unsigned comment added by 141.48.14.164 (talk) 20:11, 29 January 2011 (UTC)

The reference calls it a "classical drawing technique" and says that it is suitable for balanced trees. It also says that it is less suitable for unbalanced trees, but I don't think it's reasonable to conclude as you do that the reference calls it unsuitable for visualization in general. —David Eppstein (talk) 20:24, 29 January 2011 (UTC)

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Does not have dimension 2

The closure of the H-tree is the whole rectangle and has Hausdorff dimension 2. The H-tree itself (the union of the intervals at all scales) is not closed and has Hausdorff dimension 1, being the union of countable may sets of Hausdorff dimension 1.

The source Kaloshin-Saprykina incorrectly states on p. 6 that the H-tree has dimension 2, but correctly states in sec. 7 that its closure has dimension 2.

In Kaloshin-Saprykina, there is a whole parametrized family of H-trees with a parameter

0 < $\lambda$ ≤ 1/√2.

For $\lambda$ < 1/√2, it is useful to take the closure and you get an interesting closed set with Hausdorff dimension ranging between 1 and 2. For $\lambda$ = 1/√2, the closure is a rectangle and therefore is not in itself an interesting fractal.

This error has propagated to the article List of fractals by Hausdorff dimension. 2001:67C:10EC:578F:8000:0:0:9F (talk) 15:01, 21 November 2021 (UTC)

It is this set that defines the Hausdorff dimension of a curve. It is not true that the union of a countable number of curves necesssarily has dimension 1. –LaundryPizza03 (dc̄) 15:42, 15 June 2022 (UTC)

Alternative Construction

A way of describing the alternative construction that may help many people who are familiar with paper sizes like A3, A4, A6 etc is to talk about folding the paper in half.

This is because the sides of A4, and the others in the series have a ratio of 1: sqrt(2). So, when an A3 page is folded in half so the long side is halved, the result are 2 A4 pages connected by a fold or crease.

This can be repeated to get 4 A5 pages connected by creases/folds.

Note, an A0 sheet of paper has an area of 1 square meter. Knowing these two facts helps to explain the strange sizes of these sheets of paper. They also have the nice scaling property when printing that 2 adjacent A5 pages can fit exactly onto an A4 page.

I haven’t worked out exactly how to use this to make the description of the construction of an HTree more accessible to lay people, but it should be quite easy. CuriousMarkE (talk) 02:42, 5 November 2024 (UTC)

Not like a dendroid

Our article used to say

Topologically, an H tree has properties similar to those of a dendroid. However, they are not dendroids: dendroids must be closed sets, and H trees are not closed (their closure is the whole rectangle).

A temporary account, User:~2026-86111-3, questioned this and added a citation needed tag. Everything after "However" is easy to source, and I did source it: dendroids are compact and therefore closed; H trees are arbitrarily close to every point of the whole rectangle and therefore their closure is the whole rectangle. H trees are not the whole rectangle because they are a subset of a union of countably many lines and therefore have measure zero.

But there is actually a problem with this: it suggests that H trees have similar connectivity properties to topological trees (whether dendroids or real trees), such as that removing any point disconnects them or that any two points have a unique arc connecting them. This is false. H trees contain simple closed curves. See my new blog post https://11011110.github.io/blog/2026/04/01/htrees-not-trees.html for details. (I have no intention of adding this post as a source to our article but if someone else wants to I won't stop them.) So I am going to remove this paragraph altogether. —David Eppstein (talk) 04:34, 2 April 2026 (UTC)

Thank you! ~2026-86111-3 (talk) 09:27, 2 April 2026 (UTC)