Alternative construction of the Fibonacci word fractal. 
<dl><dd>1) From a <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\times {\sqrt {2}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>×<!-- × --></mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow></mrow></mstyle></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \scriptstyle {1\times {\sqrt {2}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7dcea590139426dcaccfa3cb5cb6b877b60e41e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:4.291ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {1\times {\sqrt {2}}}}"></span> black rectangle, remove a square whose side is <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 {2-{\sqrt {2}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mn>2</mn><mo>−<!-- − --></mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow></mrow></mstyle></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \scriptstyle {2-{\sqrt {2}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bcc5b58d45f9d0dd565dc136129d003a611a4f0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:4.291ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {2-{\sqrt {2}}}}"></span>, as shown.</dd>
<dd>2) Remove squares evenly distributed around this square as shown, with a reduction ratio of <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+{\sqrt {2}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="false" scriptlevel="1"><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>2</mn></msqrt></mrow></mrow></mstyle></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \scriptstyle {1+{\sqrt {2}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6a8e00132e51bb126b516075a78ef5c96bc87fe" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:4.291ex; height:2.176ex;" alt="{\displaystyle \scriptstyle {1+{\sqrt {2}}}}"></span>.</dd>
<dd>3) Iterate step 2 for every square generated by step 2.</dd></dl>
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