## Wednesday, November 01, 2006

### What's going on in a recursive picture?

1. Start with an image showing the frame you want to use for your Escher "Print Gallery" photograph. The highest the resolution, the better.

2. Rotate and crop the source image so that the center frame is dead in the center, and the aspect ratio of the whole image is the same as the center frame. Also, now may be a good time to correct any problem in the source image, check levels and sharpen a bit, especially the center (where the "blowing out" will be highest).

3. This step is where the mathmap magic starts to come in. By using a complex logarithm on the pixels, the image is "unrolled" around the center.
4. The previous image is cut and pasted several times, so that the whole canvas is covered.

5. This step undoes what was done in Step 3. This is done by "rolling up" the image in Step 4 by using the inverse of the complex logarithm, i.e. the complex exponential.

You might have said, why bother? I could have easily gimped the source image to get this. And you would be right. But there is more to it...

6. If you rotate the image produced by Step 4 a bit, and then roll it up as in Step 5, you get this image. Voilą!

At 1:55 PM,  Fidel said...

Wow! Thank you very much for this post.

Now I can see much better how the whole process looks like...

I am still missing all the maths, but this tutorial gives me new hopes and a good start to try to understand what the maths should do with the image.

Thanks again, you cannot imagine how much I appreciate this explanation!

Regards,
Fidel.

At 10:17 PM,  James said...

Any hope of telling us HOW to blow out the photo?

Sure "a complex algorithm" is a start, but if you're going to write a tutorial, I should be able to follow along.

At 1:30 PM,  Anonymous said...

while it's true that seb is typically thin on details, reading carefully might help some. he never wrote "a complex algorithm"...

At 8:14 PM,  N. Shields said...

Search Mathmap, a free image processing program.

At 3:50 PM,  Anonymous said...

No, he said "complex logarithm" which is pretty different but I'd still like to see it. Meh... I guess that's what google's for.