What is it ? : "Circly Koch Curve" is certainly not the "official" name of this curve. As it is composed of circles and uses an algorithm similar to the one for the Koch Curve, I gave it this name... The Parameters : Magnification step : Define how smaller will be a "son" circle compared to the parent one. Curve Order : Define the symetry of the curve. Twist parameter : Something that will mess the circles. Now I think I shouldn't have included this parameter, but it's done... I have written three transformation using this algorythm. They are more useful IMO to make "artistical" images. See Circly Koch Curve Coloring, Circly Koch Curve Mapping and Circly Koch Curve Scissor. Example :
Koch Curve
What is it ? : This formula draws the Koch Curve, one of the most famous fractal. Depending on which default gradient you have, the Koch Curve may appear all black when you load the formula. Just slide the gradient. The Parameters : With the "Inside" mode, the inside of the Koch Curve will be assigned the outside coloring. With the "Ouside" mode, the outside of the Koch Curve will be colored outside. With the "Both" mode, all the points are outside. The "Offset" parameter has no effect on the formula, but can be used to "fool" a coloring algorithm. Load for instance "Final Decomposition" in dmj.ufm, modify the offset parameter and observe the results... Maybe the two transform Koch Curve Scissor and Rotating Koch Curve Scissor will be more useful to create interesting images. Example :
Squarry Koch Curve
What is it ? : The name isn't official... It's a Koch curve made of squares instead of triangles. The Parameters : Magnification step : Define how smaller will be a "son" square compared to the parent one. Don't set this one smaller than 3. Offset : To be used with coloring algorythms. Try loading "Final Decomposition"
in dmj.ufm, modify the offset parameter and observe the results...
