Title: Petals Post by: Pauldelbrot on February 27, 2009, 02:26:14 AM (http://u5789.direct.atpic.com/25268/0/1247972/1024.jpg) (http://pic.atpic.com/1247972/1024) There is only one attractor, with period 6, for this Matchmaker Julia set, but there are parameter values close by for which there is a second. As a result, the basin is broken up by large regions of chaos that contain areas of higher iteration that resemble a disconnected classic Julia set. Essentially, the Julia set is that classic one, except extended to also bound the six-petaled structure of the attractor's basin, where the classic one has only one petal to bound as the sole attractor there is a fixed point. The single basin is colored with a gradient, from white to purple to yellow, orange, red, and black, by smoothed iterations (computed as described for Dragon II (http://www.fractalforums.com/images-showcase-(rate-my-fractal)/dragon-ii/)). As with all of these images, the actual maximum iterations setting was higher than the reported number; here I used 10,000 but the highest iteration to actually appear in the image was 100. The slow calculation is a consequence of the very aggressive antialiasing, unfortunately a frequent requirement to do justice to Matchmaker Julia set images. Freely redistributable and usable subject to the Creative Commons Attribution license, version 3.0. Detailed statistics: Name: Petals Date: February 21, 2009 Fractal: Matchmaker Julia set Location: a = 0.53256 + 0.31163i; b = -0.942843205506 - 0.343975614912i Depth: Very Shallow Min Iterations: 7 Max Iterations: 100 Layers: 1 Anti-aliasing: 3x3, threshold 0, depth 3 Preparation time: 10 minutes Calculation time: 6 hours (2GHz dual-core Athlon XP) |