Reference - formal characterization and analysis of Koch curve

Question

I am studying the Koch curve but most resources I have seen do not describe the Koch curve formally and are similar to the Wikipedia page on the subject. For example, I have looked at books like Fractal Geometry by Falconer and Measure, Topology, and Fractal Geometry and found it difficult to build formal proofs based on those constructions.

Does anyone know of a book or accessible paper that discusses the Koch curve and its properties formally?

If you could also refer me to a resource that discusses generalized Cantor sets and Cantor functions with proofs of some of the properties I would really appreciate it.

For the Koch curve, see the references I gave in my answer to Why does the Hilbert curve fill the whole square?. For Cantor functions, see the references I gave in my "question" Bibliography for Singular Functions. For Cantor sets, Sergio Eugenio Plaza's 1992 manuscript Numerical invariants of Cantor sets might be helpful. — Dave L. Renfro, Jul 07 '14 at 15:54
Also, for Cantor sets see Robert W. Vallin's recent book The Elements of Cantor Sets: With Applications. I can't believe I forgot about Vallin's book, since he and I finished our Ph.D.'s under the same person at about the same time (thus, we were in several classes and seminars together) and a few months ago I spent a lot of time writing up an Errata/Suggestions list (but I'm only a third through his book at this time). — Dave L. Renfro, Jul 07 '14 at 16:16

score 1 · Accepted Answer · answered Jul 05 '14 at 17:52

Rigorous and self-contained treatment of self-similar sets, including both Koch snowflake and Cantor-type sets, can be found in the excellent book Geometry of Sets and Measures on Euclidean spaces by Mattila.

Reference - formal characterization and analysis of Koch curve

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