Hand drawn fractal and how to make it an algorithm?

[raphuu]

[sorry for triple post, but each time i try to add a picture to the post, i get a server internal error, and then the post is unreadable]

Hi folks,

I am a visual artist. I have been following this forum since the Mandelbulb story with great interest.

Lately, I have been experimenting with some procedural drawings with a compass which lead to, imho as a non-mathematician/programmer, a kind of fractal (examples attached). I am looking for a way to put it into algorithms so that a software can draw it. I'll be happy if someone could help me on that or at least tell me if it is feasible or not.

thank you!






To produce it, it goes like this:

On a sheet of paper,

Initialisation:

chose an arbitrary initial point.
chose an arbitrary radius
trace an arc of arbitrary length (but > 180°).

Iteration (first one):

Open the compass to the length between the two ends of the first arc.
put the spike of the compass on one end of the first arc (new center).
trace the second arc. its length is defined by the line of the first one, i.e. the line acts as hard boundary.

Iteration (rest):

Open the compass to the length between the two ends of the last arc.
put the spike of the compass on the end of the last arc which is closer to the center of the very first arc.
trace a new arc. its length is defined by the line of the other, already drawn, ones. when several possibilities exist, trace where there is the most place, i.e where you can draw the longer line.

Remarques:
1) if the line goes out of the sheet of paper and cannot come back in again, its length is taken from the border of the sheet.
2) if the line goes out of the sheet of paper and can come back in again, then the missing part of the arc is taken into consideration when looking for the longer line possible.

[kram1032]

For the reason you mentioned already (strange O.o), there actually is no image.
However, just by what I have in mind, according to your descriptions, I got it like the second always is a circle, as when you put the compass needle into the end of the first arc and draw a second arc from one "wall" to the next, this is the very same place for beginning and end, directly on the first arc...

By far not as beautiful as it probably would be if I used a compass, but I tried some letter-based fractals by hand (and in these particular examples by mouse, so they are pretty wonky^^)
but look yourself if you're interested
http://kram1032.deviantart.com/gallery/#Tutorials

[raphuu]

However, just by what I have in mind, according to your descriptions, I got it like the second always is a circle, as when you put the compass needle into the end of the first arc and draw a second arc from one "wall" to the next, this is the very same place for beginning and end, directly on the first arc...

thank you for the answer, and you are right. I forgot the step where after each iteration you open the compass to the length of the previous arc. (edited in original post).

I'll post images later on with a link to an external site… done.

[kram1032]

Ah, I see

Great images, very wild pattern