The Fibonacci word fractal as an iterated construction of octogons. The size of each octogon <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 {={\sqrt {2}}-1}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow><mo>−<!-- − --></mo><mn>1</mn></mrow></mstyle></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \scriptstyle {={\sqrt {2}}-1}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a5845948a4da6c1a681ca169806c184ce469201" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:5.57ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {={\sqrt {2}}-1}}"></span> times the size of the previous iteration. They turn, alternatively, on the left and on the right of the previous octogons. The number of octogons = 4 times a Fibonacci number.
<a href="//commons.wikimedia.org/wiki/User:Prokofiev" title="User:Prokofiev">Prokofiev</a>
CC BY-SA 3.0
<span class="int-own-work" lang="en">Own work</span>