Dendrite (mathematics) explained

In mathematics, a dendrite is a certain type of topological space that may be characterized either as a locally connected dendroid or equivalently as a locally connected continuum that contains no simple closed curves.^[1]

Importance

Dendrites may be used to model certain types of Julia set.^[2] For example, if 0 is pre-periodic, but not periodic, under the function

f(z) = z ^{2} + c , then the Julia set of f is a dendrite: connected, without interior.^[3]

See also

• Misiurewicz point
• Real tree, a related concept defined using metric spaces instead of topological spaces
• Dendroid (topology) and unicoherent space, two more general types of tree-like topological space

Notes and References

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