I am trying to understand Levy walk. I went through the wiki page and there was a line saying:
A Lévy flight is a random walk in which the steps are defined in terms of the step-lengths, which have a certain probability distribution, with the directions of the steps being isotropic and random.
I am unable to understand the part
with the directions of the steps being isotropic and random.
Doesn't the terms isotropic and random have a completely different meaning?
Note: If possible, it would be of great help if you can provide more tutorials to understand levy walk easily.
Random --> a direction is chosen randomly to a take a step in (on the unit sphere as @Did mentions)
Isotropic --> there is no difference in how the different directions are treated. I.e. the probability distribution from which the step-length is chosen would be the same regardless of the step-direction chosen (chosen randomly in your example).
See (taken from: https://www.quantamagazine.org/random-search-wired-into-animals-may-help-them-hunt-20200611/):