<b><a href="//commons.wikimedia.org/wiki/Julia_set" title="Julia set">Julia set</a></b>, a <a href="//commons.wikimedia.org/wiki/Fractal" title="Fractal">fractal</a>, here in three dimensions. The image was created from using a "iterated function system". This is not a quaternion - only three parameters; x, y, z was used in the reversed formula <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 Z=sqrt(Z-C)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>Z</mi><mo>=</mo><mi>s</mi><mi>q</mi><mi>r</mi><mi>t</mi><mo stretchy="false">(</mo><mi>Z</mi><mo>−<!-- − --></mo><mi>C</mi><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle Z=sqrt(Z-C)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e694772c2e5f6e9bf51a2d822a3e44e9b4fd7913" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:16.924ex; height:2.843ex;" alt="{\displaystyle Z=sqrt(Z-C)}"></span>. In 2D the root function rotates to half the previous angle and scales to the root of the previous length. I developed a method to do this using three parameters, (see formula in C-code below).
<a href="//commons.wikimedia.org/w/index.php?title=User:Solkoll&amp;action=edit&amp;redlink=1" class="new" title="User:Solkoll (page does not exist)">user:Solkoll </a>
<span class="int-own-work" lang="en">Own work</span>