Talk:H tree

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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)[reply]

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)[reply]

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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)[reply]

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 (d c̄) 15:42, 15 June 2022 (UTC)[reply]