How to program a dragon curve?
How to program a dragon curve?
A Dragon curve is a recursive non-intersecting curve also known as the Harter–Heighway dragon or the Jurassic Park dragon curve. It is a mathematical curve which can be approximated by recursive methods such as Lindenmayer systems….Heighway’s Dragon Curve using Python.
| Dragon Curve L-System | |
|---|---|
| variables: | f h |
| constants: | + – |
| axiom: | f |
| rules: | f = f-h h = f+h |
What is the dragon curve used for?
The dragon curve can tile the plane. One possible tiling replaces each edge of a square tiling with a dragon curve, using the recursive definition of the dragon starting from a line segment.
How does the heighway dragon works?
The Heighway dragon is constructed by replacing a line segment with two segments at 45°. If the angle between the line segments is less than 45° then a different dragon curve will be formed. If we let the angle grow from 0° to 45°, we can watch the Heighway dragon being born. See the animation.
How do you make a fractal tree?
Here is the basic plan for this tree fractal:
- Start at some point and move a certain distance in a certain direction.
- At that point, make a branch. Turn some angle to the right and then repeat the previous step with a shorter distance. (Recursion!)
- Now go back and turn left to make the other branch. (Recursion again.)
Who invented dragon curve?
John Heighway
The dragon curve fractal has the shape of a giant dragon, but it’s made up of one line that bends back and forth, which creates what looks like a bunch of boxes. The dragon curve fractal was invented in 1966 by John Heighway and William Harter. Heighway and Harter were both NASA scientists.
Is a tree fractal?
Trees are natural fractals, patterns that repeat smaller and smaller copies of themselves to create the biodiversity of a forest. Each tree branch, from the trunk to the tips, is a copy of the one that came before it.
Is the Fibonacci spiral a fractal?
The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal.
What is the dimension of the dragon curve?
dimension 2
The dragon curve is a space filling curve with dimension 2 which originally came from the repeated folding of a long strip of paper in the same direction [4). After pleating the paper, it is then unfolded with each adjacent segments of paper formed into a right angle.
Why is Sierpinski’s Triangle a fractal?
The Sierpinski triangle is a fractal described in 1915 by Waclaw Sierpinski. It is a self similar structure that occurs at different levels of iterations, or magnifications. This pattern is then repeated for the smaller triangles, and essentially has infinitely many possible iterations.
What kind of curve is the dragon curve?
A Dragon curve is a recursive non-intersecting curve also known as the Harter–Heighway dragon or the Jurassic Park dragon curve. It is a mathematical curve which can be approximated by recursive methods such as Lindenmayer systems.
How to draw a dragon curve by Sarah Bricault?
% This function draws a Dragon Curve (or a variant of that curve) with the % following inputs: % iterations = int; number of iterations % makeVideo = 1 or 0; set to 1 to make a video % xlimVals = [xmin,xmax]; set the x-boundaries for the graph % ylimVlas = [ymin,ymax]; set the y-boundaries for the graph
How to make a finite approximation of the dragon curve?
Move forward (in the dir of the current heading) a distance d while drawing a line of color c. The state of the turtle changes to (x’, y’, a, c), where x’ = x + d cos (a) and y’ = y + d sin (a) The finite approximation of Dragon curve can be created with an L-System.The Dragon curve L-system can be represented as :
How to make Heighway’s dragon curve using Python?
Unfold the strip and make a firm crease along each of the fold lines, taking care to maintain the correct direction for the fold. Stand the strip on its edge, with each fold forming a 90 degree angle, and look down on it. You will see an intricate pattern of squares, and twists and turns.