#Dragon curve ultra fractal how to

In the next step I will show how to automate this task and draw it using python. This way we find that the 4th iteration can be represented as RRLRRLLRRRLLRLL. Lets try this out to to find the 4th iteration from the 3rd: Add the flipped version to the new string we made in the first step Take the flipped version and switch all the rights to lefts and the lefts to rightsĤ. Take the original string and flip it backward (first character last, last first)ģ. In order to find the next iteration from one you already have:Ģ. There are many more ways of generating the Curve, but I will be focusing on this method. You can therefor generate different iterations of the Dragon Curve by generating these strings. You can represent each iteration as a string of right and left turns.Īnd so on. Looking at the above pictures, you can see that the Curve is made of multiple segments at right angles.

$dragon curve ultra fractal$

From my personal observations, it seems to turn 45 degrees clockwise every iteration. They are all more complex than the last, but all have the same shape, though different orientations. Above are the 2nd, 4rd, 6th, and 8th iterations of the Dragon Curve. The Dragon Curve, like all fractals, has multiple, progressively more complex forms, called iterations. In this Instructable, I will be showing you how to write a python 3 program using the turtle graphics module to generate the Dragon Curve.

$dragon curve ultra fractal$

Here are some sites that can tell you more: If you take all the solutions to polynomials with coefficients in a certain range and graph them on an complex plane, you will find the dragon curve in places If you take a strip of paper and fold it in half, then fold that in half, and that in half, and so on, and then unfurl it, you will get a Dragon Curve That line never goes over itself, so theoretically one big enough can hit every single point in a grid exactly once Even if it doesn't look like a dragon to you, you must admit it's a cool name.Īnd it's not just the name, or the shape, the Dragon Curve has lots of amazing properties: The Dragon Curve gets it's name for looking like dragon, perhaps a sea dragon (apparently). It is actually a family of self-similar fractals, but I will be focusing on the most famous, the Heighway Dragon, named after one of the NASA physicists who studied it, John Heighway. The Dragon Curve is an interesting and beautiful fractal.

$dragon curve ultra fractal$