The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets · HackerPapers discussionshttps://hackerpaper.kaipfister.de/p/math_9201282/Collected HN comments and submissions linking this paper.enMon, 02 Nov 2026 11:16:22 GMTThe Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets — mentioned by oarabbus_https://news.ycombinator.com/item?id=21887964urn:hackerpapers:mention:math_9201282:21887964Fri, 27 Dec 2019 00:06:38 GMT<p>&gt;There is a common misconception, repeated here, that fractals are defined by their self-similarity. This is not a misconception. Self-similarity at all length scales is indeed a defining factor of fractals. From that fact it _does_ follow that _most_ fractals have a non-integer fractal dimension. However it is absolutely not true that fractals have non-integral dimensionalities; for example the most famous fractal of them all, the Mandelbrot set, has an integer Hausdorff dimension of 2. [0] https://arxiv.org/abs/math/9201282</p><p><a href="https://hackerpaper.kaipfister.de/p/math_9201282/">Paper and discussion history</a>. A mention is not an endorsement.</p>math.DS