Dendrite (mathematics)

Template:Short description 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.

Dendrite Julia set

Importance

Dendrites may be used to model certain types of Julia set. 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.

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

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