Information about Exponential Tree
An exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimension (d) of 1, and has 2d children. In an exponential tree, the dimension equals the depth of the node, with the root node having a d = 1. So the second level can hold two nodes, the third can hold eight nodes, the fourth 64 nodes, and so on.
In fact, this method of laying out a tree can be viewed as an application of the upper half-plane model of hyperbolic geometry, with isometries limited to translations only.
Layout
"Exponential Tree" can also refer to a method of laying out the nodes of a tree structure in n (typically 2) dimensional space. Nodes are placed closer to a baseline than their parent node, by a factor equal to the number of child nodes of that parent node (or by some sort of weighting), and scaled according to how close they are. Thus, no matter how "deep" the tree may be, there is always room for more nodes, and the geometry of a subtree is unrelated to its position in the whole tree. The whole has a fractal structure.In fact, this method of laying out a tree can be viewed as an application of the upper half-plane model of hyperbolic geometry, with isometries limited to translations only.
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See also
binary search tree (BST) is a binary tree data structure which has the following properties:
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- Each node has a value.
- A total order is defined on these values.
- The left subtree of a node contains only values less than the node's value.
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fractal.]]
A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity.
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A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity.
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In mathematics, the upper half-plane H is the set of complex numbers
with positive imaginary part y. Other names are hyperbolic plane, Poincaré plane and Lobachevsky plane, particularly in texts by Russian authors.
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with positive imaginary part y. Other names are hyperbolic plane, Poincaré plane and Lobachevsky plane, particularly in texts by Russian authors.
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hyperbola (Greek ὑπερβολή literally 'overshooting' or 'excess') is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves
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