Dragon Fractal Applet

Instructions

Basically, you just pick your options, hit the "Draw Fractal" button, and see what happens.

The controls are pretty simple:

Iterations: This controls how much of the fractal to draw. This can be any number greater than or equal to zero. Each iteration draws twice as much fractal as the iteration before it. Iterations above 10 or so can take a while to draw.
Size: This is the length of each line segment in the fractal. It should be at least 1.
Origin X: This is the horizontal distance, in pixels from the left edge of the applet area, that the applet starts at when it draws the fractal.
Origin Y: This is the vertical distance, in pixels from the top edge of the applet area, that the applet starts at when it draws the fractal.
Background Color: Select the color you want for the background.
Draw Mode: This controls the way the fractal is drawn on the screen.
- Plain: Just draws the fractal in black.
- Midpoints: Draws lines through the midpoints of the lines from the plain fractal. Result is a neat looking maze.
- Mirror Alternations: Draws the fractal in alternating blue and yellow, switching colors at an iteration boundary.
- Color Cycle: Alternates through 8 colors as it draws the fractal. Looks pretty ugly, actually.
- Left/Right Colors: Draws the fractal in black if the pen turns left, and in white if it turns right at the end of the current line segment.
- NEWS Colors: Draws white if moving North, black if moving East, blue if moving West, and red if moving South.
- Fade 1: Fades from black to white over the length of the fractal
- Fade 2: Fades from blue to white between the mirror points. This is my personal favorite.
- Color Cycle 2: Just like the first color cycle, but with only 7 colors. Looks even uglier than the other Color Cycle, if that's possible.
- Fade 3: Fades from green to white over a regular interval.
- Filled Squares: Just draws the squares, filled in red.
- Filled Squares 2: Draws the filled squares, fading from blue to yellow over the length of the fractal.
- Filled Squares 4: Draws the filled squares. The shade of the square depends on which corner was the last one filled, or something like that.

I will be adding features when I have the time. There's a bunch of things I'd like to do with this applet including more drawing styles and more control over the colors used. If you have any suggestions, please feel free to send them to me!

About The Dragon Fractal

The dragon is a fractal that first came to my attention when I read Jurassic Park by Michael Crichton. The book was divided into sections called "iterations", each of which featured a drawing of a fractal that grew at each stage. I took it upon myself to figure the fractal out, which took me a few days playing on my computer. The fractal is generated by drawing a line segment and then turning left or right before drawing the next one. The key, of course, is figuring out the sequence of left and right turns.

The first step is to pick a "mirror" turn. I use left in this applet. The first turn in the sequence is the mirror. Then for each iteration:

Put the mirror at the end of the current turn sequence.
Reverse all the turns that came before the new mirror in both order and direction (LLLR becomes LRRR) and put them on the end of the turn sequence.

Here's how it works in practice. We'll use "L" for left turns and "R" for right turns. Red "L"s are the current mirror

L	(starting position)
LL	(add the mirror)
LLR	(reverse and invert all turns before the mirror, first iteration done)
LLRL	(add the mirror)
LLRLLRR	(reverse and invert all turns before the mirror, second iteration done)
LLRLLRRL	(add the mirror)
LLRLLRRLLLRRLRR	(reverse and invert all turns before the mirror, third iteration done)
LLRLLRRLLLRRLRRL	(add the mirror)
LLRLLRRLLLRRLRRLLLRLLRRRLLRRLRR	(reverse and invert all turns before the mirror, fourth iteration done)