Fractal curve created by Benoit Mandelbrot and published in "Penser les mahématiques", éditions du Seuil (1982) as an example of a space-filling curve. Its Hausdorff dimension is 2. It is built from 7 simililarities of ratio 1/3 and 6 similarities of ratio <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \scriptstyle {1/3{\sqrt {3}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>3</mn><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>3</mn></msqrt></mrow></mrow></mstyle></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \scriptstyle {1/3{\sqrt {3}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01367cb88edc6cd6dfd41066a8578fd6fc29793a" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:4.657ex; height:2.343ex;" alt="{\displaystyle \scriptstyle {1/3{\sqrt {3}}}}"></span>. This image displays the curve after 2 iterations.
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