The paperCrane’s view from the reverseFold

On the way home last Thursday I decided to try creating fractal letters. The idea was to replace each “line” in a simple version of a letter with a copy of itself but allow for the aspect ratio of its dimensions to change so that the result is still recognizable as a letter. This is something like an L-system, of which the Dragon curve is one. After a weekend’s worth of work I have what amounts to thirteen different fractal letter algorithms for six different letters. 1 P, 3 A, 2 E, 2 R, 2 C, 3 N. Yes, those spell PAPERCRANE. Here is the first iteration (just the letters).

Fractal Letters, iteration 1

And here is the fifth iteration:

Fractal Letters, iteration 5

Some letters have variations in how they are drawn or how they repeat, or both (hence the 2 lines). The bottom N uses an algorithm I worked out which didn’t change the aspect ratio and had only one repetition per line. Both of the N variants in the words use two repetitions per line and constrict the width faster than the height, which leaves the N recognizable. The idea here, after all, was to make letters which had a cool fractal look but could still be read.

Click either of the pictures to view the flex app and play with the iterations yourself. Just drag (or click on) the slider on the bottom of the app to change the iteration.

Stay tuned, I have another blog post coming up soon specifically about that N on the bottom, the math required to create the algorithm, and some interesting (and beautiful) results I got when implementing a test program.

Over the Christmas break I went to Chinatown in San Francisco and got some new origami paper which is smaller than any of my other paper. I quickly decided to make one of my signature reversefolds with the new paper. I started creasing the paper and got to the sane point, which would have given me 4 rows of reversefolds. This would have been small, but not small enough for me. I like my folds to be more complicated.

Finished creases, back side

Finished creases, front side

Yes, that paper is less than 2 quarters wide. Of course, going one more level took a lot of careful and precise folding which took the rest of the night. The next day I started the accordion folds which are the base of the final product.

Accordion halfway done

Accordion finished

That took several hours. The last step is to pop in the reverse folds, one row at a time. This is the most time consuming part of the process and for this fold it took me several nights with a small crafting tool. Here it is with five rows finished.

Five rows finished

And after many painstaking hours of work, here is the finished product:

Finished fold

Finished fold, side view

Finished fold, 3/4 view

And for a little perspective here is a shot of the finished fold compared to the original paper:

Finished fold vs. unfolded paper

And just in case the quarter wasn’t enough, here’s the finished fold in my palm. Yes, it is that small. No, I won’t make you one. ;-)

Finished fold in the palm of my hand

All of these photos link to my newly created flickr account. The entire set is up there along with higher quality versions.