Dani Laura (they/she/he)<p>1/2<br>I have devised a procedure for creating a novel kind of iterative fractals, based on sectors of circumference (they cannot be produced by segments). For each sector, defined by a point, a radius, and two angles (see second picture), a substitution is defined producing a sequence of sectors. In that image, a substitution is shown which produces three new sectors, based on the parameter 𝛽, the middle portion of the original sector which is replaced with a new sector with smaller radius spanning half a turn. The lateral sectors are reduced in spread but not in radius. The first picture shows a subfractal produced when 𝛽 = 1/3, starting with a sector which spreads a full turn. The third picture shows an artistic rendering of the same fractal, where just the initial sector (a circle) and the newly added semicircles are drawn.<br>Next post will show further versions.</p><p><a href="https://mathstodon.xyz/tags/Mathart" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathart</span></a> <a href="https://mathstodon.xyz/tags/Fractal" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Fractal</span></a> <a href="https://mathstodon.xyz/tags/geometry" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>geometry</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/algorithmicArt" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>algorithmicArt</span></a> <a href="https://mathstodon.xyz/tags/NotAI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>NotAI</span></a></p>