11/2/2022 0 Comments Dragon curve ultra fractal![]() ![]() ![]() Count the number of bends to determine the degree. It's from an outfit named DragonNerd in Winnipeg. I found this at an on-line shopping center named Etsy, in the "Fractal and Geeky Jewelry" section. It turns out that as both the degrees and the translates go to infinity, the curves, which are intricately intertwined, never intersect, and completely cover and tile the complex plane. We could now do translations in all four compass directions and superimpose all the dragons, but I won't show that. Rotate the entire dragon by $90^\circ$, superimpose it on the original, and plot the four halves with four colors. More folds do not change any more pixels. In polar form, $w$ is $e^$ short line segments and have reached the limits of screen resolution. This is done with the help of the complex number w = (1 i)/2 When we plot z, we get a single black line, representing an unfolded strip of paper. This isn't complex yet, but it soon will be. The computations are based on a growing and shrinking vector z of points in the complex plane. The following figures are all from my new MATLAB program, dragon. RRLRRLLRRRLLRLLRRRLRRLLLRRLLRLLRRRLRRLLRRRLLRLLLRRLRRLLLRRLLRLL That flips the string s end to end and replaces all the R's by L's and the L's by R's. DRAGON CURVE ULTRA FRACTAL CODEThe key operation in the code is LR-fliplr(s). That's all I can display in one column of this blog post. Here's code to display the signatures of degrees one through six. To change the start hue value move the slider The second way is to turn off HSL and use the colour picker to choose a start and end colour. The colour hue changes through each iteration. When turned on, a bright set of colours is used. The number of segments between folds doubles with each increase in degree. There are two ways to colour the fractal, the first is to use the HSL setting. ![]() The degree three signature is RRLRRLL.Ĭan you read off the signature of degree four from the photo? Do you see the pattern? Probably not yet. The degree two curve has two right angles, followed by a left that's RRL. The degree one curve has one right angle let's denote that by R. How many times do you imagine you could fold the paper before it is too thick to fold again? Probably five, maybe six. You will have created a Dragon Curve of degree four. Unfold the strip so that all the folds form the right angles pictured. Then fold it a second time, being careful to fold in the same direction, right over left or left over right, as the first. Start with a long, narrow strip of paper, like the one in the following photograph. ![]()
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