Turning into Turing

Rotational Growth in Photoshop®

I stumbled into this one while working on a different project where I scripted the rotation of an image in preparation for an animation. When I looked at the last frame though, I noticed the image looked washed out and with odd patterning. Some sort of generation loss was happening to the image and I remembered previous exmaples of exploiting and celebrating the degradation process, like Alvin Lucier’s I Am Sitting in a Room, saving a jpeg hundreds of times, and the like and knew I needed to push the rotational distorion as far as I could.

The Inquiry:

Let’s use this image of a rainbow gradient:

and rotate it 72 times in 5 degree increments so we’ve done a full rotation and should be back to the original:

As you should be able to see in the animation, the gradient no longer looks the same after 360°. If we then take only the frames from multiples of 360°, the image begins to grow and show the characteristics of a Turing pattern:

Depending on the interpolation method you use, a different result occurs.

Interpolation differences

We’re going to mostly ignore Bileaner and Nearest Neighbor after this first set as they don’t produce Turing patterns.

Interpolation algorithm	5° 72 iterations / 1 revolution (360°)	5° 3240 iterations / 45 revolutions (16200°)
Bicubic
Bicubic Sharper
Bicubic Smoother
Bilinear
Nearest Neighbor

Degrees per rotation differences

Let’s have a look at how the patterns change based on the degree that you execute each rotation iteration. I’ve done all the integer degrees that evenly split 360º as well two small decimal degrees. Note that rotating by 90° or 180° have no effect as they are lossless transformations.

Rotation Info	Bicubic	Bicubic Sharper	Bicubic Smoother
0.25° 1440 iterations 1 revolution 360°
0.25° 4320 iterations 3 revolutions 1440°
0.5° 720 iterations 1 revolution 360°
0.5° 3600 iterations 5 revolutions 1800°
1° 360 iterations 1 revolution 360°
1° 3240 iterations 9 revolutions 3240°
2° 180 iterations 1 revolution 360°
2° 3240 iterations 18 revolutions 6480°
3° 120 iterations 1 revolution 360°
3° 3240 iterations 27 revolutions 9720°
4° 90 iterations 1 revolution 360°
4° 3240 iterations 36 revolutions 12960°
5° 72 iterations 1 revolution 360°
5° 3240 iterations 45 revolutions 16200°
6° 60 iterations 1 revolution 360°
6° 3240 iterations 54 revolutions 19440°
8° 45 iterations 1 revolution 360°
8° 3240 iterations 72 revolutions 25920°
9° 40 iterations 1 revolution 360°
9° 3240 iterations 81 revolutions 29160°
10° 36 iterations 1 revolution 360°
10° 3240 iterations 90 revolutions 32400°
12° 30 iterations 1 revolution 360°
12° 3240 iterations 108 revolutions 38880°
15° 24 iterations 1 revolution 360°
15° 3240 iterations 135 revolutions 54600°
18° 20 iterations 1 revolution 360°
18° 3240 iterations 162 revolutions 58320°
20° 18 iterations 1 revolution 360°
20° 3240 iterations 180 revolutions 64800°
24° 15 iterations 1 revolution 360°
24° 3240 iterations 216 revolutions 77760°
30° 12 iterations 1 revolution 360°
30° 3240 iterations 270 revolutions 109200°
36° 10 iterations 1 revolution 360°
36° 3240 iterations 324 revolutions 116640°
40° 9 iterations 1 revolution 360°
40° 3240 iterations 360 revolutions 129600°
45° 8 iterations 1 revolution 360°
45° 3240 iterations 405 revolutions 54600°
60° 6 iterations 1 revolution 360°
60° 3240 iterations 540 revolutions 109200°
72° 5 iterations 1 revolution 360°
72° 3240 iterations 648 revolutions 116640°
120° 3 iterations 1 revolution 360°
120° 3240 iterations 1080 revolutions 109200°	what’s this guy doing?!?

Single Color

I think the pattern that Bicubic makes is the same no matter what color is being used (to research more), while the other two are different based on color

Rotation Info	Bicubic	Bicubic Sharper	Bicubic Smoother
5° 72 iterations 1 revolution 360°
5° 3240 iterations 45 revolutions 16200°

Two Colors

When two flat colors are used, there is an interesting reaction based on the differences between the RGB values of the two colors.

Rotation and color info	60 iterations / 1 revolution (360°)	Correlation of RGB values	3240 iterations / 54 revolutions (19440°)
6° Red & Magenta		only the two colors
6° Red & Yellow		only the two colors
6° Green & Yellow		only the two colors
6° Blue & Magenta		only the two colors
6° Red & Dark Red		only one color and black
6° Green & Light Green		only one color and white
6° Red & Blue		the two colors, their secondary color, and black
6° Green & Blue		the two colors, their secondary color, and black
6° Red & Green		the two colors, their secondary color, and black
6° Green & Magenta		the two colors, white, and black
6° Blue & Yellow		the two colors, white, and black
6° Greyish & Salmonish		primary colors, secondary colors, white, and black
6° Greyish & Salmonish (16-bit color)		primary colors, secondary colors, white, and black

Has somebody already done this?

Since this is one of those super simple things that anyone can do—they just need to be the first to find it,—I was worried I had spent a whole bunch of time repeating something someone else had done already. I was also aware of other projects that use repeated actions to expose generational loss that I mentioned earlier, but nothing that focused specifically on rotation as the impetus, and nothing that ended up with Turing patterns. After some cybersearching, I could only find things that were close, but nothing that hit on the Turing pattern aspect.

I think the closest was all the way back in 1999 when Helmut Dersch tested the quality of different interpolation algorithms by rotating images in 5° increments 36 times to 180° of the original (I chose 5° for my original samples in their honor). I am including a resampling of the images they used in the tests to give a look at what Helmet might have discovered back then. The second closest was a variation on something I was aware of (resaving jpegs), rotational jpeg compression. Here I think the degradation relies more on the unique qualities of jpegs, and doesn’t result in the novel patterning.

I did also come across another artist who found a way to make Turing patterns in Photoshop® using repeated blurring and sharpening of images. Given the way this method works, you have much greater control over the resulting Turing pattern. My method relies on the reaction-diffusion system happening at a pixel level, and so the variety of end results is pretty limited.

Revising Helmet Dersch’s tests	Monument	Test	Ken Turkowski’s Zone Plate
The original images
Same settings as original experiment, except 1° instead of 5° Bicubic, 1° 180 iterations 0.5 revolutions 180° then flipped 180°
Bicubic, 5° 72 iterations 1 revolution 360°
Bicubic, 5° 3240 iterations 45 revolution 16'200°
Bicubic Sharper, 5° 72 iterations 1 revolution 360°
Bicubic Sharper, 5° 3240 iterations 45 revolution 16'200°
Bicubic Smoother, 5° 72 iterations 1 revolution 360°
Bicubic Smoother, 5° 3240 iterations 45 revolution 16'200°

A note about the size of the images on this page:

The rotated images often contain a vast network of pixels that extend around the visible patterns. These pixels are about 99% transparent, making them virtually imperceptible. They also added a lot of extraneous bloat to the page. As a fix, I have trimmed many of the resulting images to only show the visible pixels. I'm including here an example of the true extent of one image and, to show the hidden network of pixels, another version where I have taken all pixels that are not completely transparent and made them 100% opaque.

Rotation Info	Original result of rotations	Original with transparency made opaque
Bicubic, 5° 3240 iterations 45 revolutions 16200°

What about if we rotate the image 5 degrees and then immediately rotate it -5 degrees over and over?

Interpolation algorithm	72 iterations	3240 iterations
Bicubic Sharper

Or rotate 5 degrees for one full revolution (360°) and then rotate it -5 degrees for a full revolution (-360°)?

Interpolation algorithm	144 iterations (since 72 wil be the same as original)	3240 iterations
Bicubic Sharper	back and forth original