Dendrite (mathematics)

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]

Dendrite Julia set

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