And that color, was orange.

“I call these, ‘Bronze Shields,’” he told the Flickr group in October 2004. He posted the images he’d created in the group’s site and they did indeed, look something like orange-y, dirt-tarnished shields.

“It looks like the beginnings of a nice pizza pie,” said Striatic, the moderator of the group.

The comments on Flickr rolled in but no one could figure out why the orange was ubiquitous. There were a lot of pictures of the sky on Flickr, people pointed out, but stubbornly, the shields refused to average to blue. Bumgardner made a lot of bronze shields—each using 25 or more original photos from the Squared Circles pool. He found that the more photos he used, the more reliable the effect was. “I thought it might be a bug,” he explained, “That there was some flaw in the my algorithm.”

Bumgardner’s algorithm averaged the photos by looking at the different red, green, and blue (RGB) components of the pixels of the images. Each color of a photo corresponded to a number, ranging from 0-360 degrees on the color wheel. For instance, one spot on an image might be coded as (10, 67, 111). Bumgardner’s algorithm would take these RGB values, add up the Rs, the Gs, and the Bs, and divide by the number of images used. This would create the composite image with the average color from every spot on each photo. But it wasn’t the algorithm that was off—orange was the result.

Maybe it was something about squared circles, Bumgardner thought. So he went to another Flickr group. And another. And another. And he found that images across all of Flickr yielded the same thing, with the caveat that the group wasn’t already devoted to a color-based topic like only blue images.

“It wasn't until I started looking at photos in other Flickr groups that I realized the phenomenon was more pervasive,” he said. Bumgardner tested it with Instagram photos and Google images and came up with the same thing. When someone told him that it was probably due to the colors of flesh in photographs, he tried it with a pool of graffiti. Still orange.

* * *

Bumgardner looks more like a retired wrestler, softened by time and two kids, than a man who constructs mazes and sudokus in his free time. Balding slightly with groomed facial hair (mustache, beard, soul patch), he isn’t the typical tight-jeaned, hoodie-covered nerd wandering around the West Coast. In his own words, “When I walk, I bounce a bit on each step, like a finch in flight.”

For someone who thrives on bewildering avid puzzlers, Bumgardner’s past is surprisingly straightforward. He was always a nerd as a kid, reading fantasy books in the lower bunk of his bed while his brother, the jock, was out playing. Growing up he believed computers were, “evil things that were foisted on us by huge corporations,” an idea he got from the media of the 1970s. Needless to say, he wasn’t interested in them as a kid. He wanted to do art. It wasn’t until he went to CalArts and bunked with a computer programmer, Kevin Bjorke, that he got into “recreational programming” and did it, “with great abandon.” He learned Javascript, Python, C, C++, PHP, Processing, Java, Perl, and Flash, among others.

He and Kevin were also into A. K. Dewdney, a mathematician who wrote the Recreational Programming column for Scientific American at the time. The two would devour his columns and then create their own programs. Bumgardner’s log of his interests, which he’s kept for nearly 30 years, reflects the obsessions of his youth. Ordered by month and year, the log starts in 1985 with “Time-based C-Dialect for communications program.” It goes on from there, reading somewhere between a Best Buy inventory and a grocery list:

07/90 Computer Chess

03/95 Cheese Toast II

04/99 WinAmp

08/07 Crop circles

01/13 Loose Leaf Tea

It also charts his growing interest in puzzles—from chess and crosswords to sudokus and mazes. Bumgardner, who says he is is mildly bipolar, also uses the list to keep track of his peaks and troughs. However, unwittingly, it also tells the story of his discovery. In 2005, he writes:

01/05 FLICKR, Squared Circle, Photomosaics, Bronze Shields <-- PEAK

He confirmed later that he was going through a peak at the time and experienced a burst of creative productivity that he says led to the uncovering of emergent orange.

* * *

After unearthing emergent orange, Bumgardner dug around for outside explanations of what it might mean. Maybe it was the chemical compositions of things in nature; maybe if you created a bunch of synthetic, abstract digital images and averaged them together, they wouldn’t average to orange.

But they did. It was always orange.

In fact, the only way Bumgardner could avoid orange was by generating his own artwork with a pseudo-random number generator.

After a 2006 blog post on the subject, Bumgardner’s list grows quiet on the topic for a number of years. Then, in September 2012, popular YouTube personality Ze Frank published a video that showed emergent orange in action.

Bumgardner and three mathematically-inclined contacts emailed enthusiastically about the video and other theories, one of them exclaiming, “I’m excited that this is back on. Keep in touch!” He finally wrote his own informal, non-peer-reviewed paper on the phenomenon at the end of 2013.

Bumgardner posited that the ever-present orange was caused by chemistry and physics. The averaged photos, he suggested, were actually acting like a mass spectrometer, “reflecting the average chemical composition of the subjects being photographed.” Of course, not everyone agreed with this theory.

The theoretical neurobiologist Mark Changizi suggested it might be “some funny artifact of how images are coded and/or how the averaging is done.” Dave Chappell, a physicist at the University of La Verne, guessed that Bumgardner might be onto something with the way humans perceive color. Craig Kaplan, a researcher in the Computer Graphics Lab at the University of Waterloo, told me, “in the years since Bumgardner produced his first bronze shield, I have not yet seen a convincing explanation for emergent orange.”

“You ask five different people what causes it,” Bumgardner says, “You’ll get five different answers.”

Emergent orange became a colloquial Rorschach test. A photographer would say it was something with the cameras. A physicist would say it’s all about the light. A psychologist might comment on human perception. “Maybe they’re all right,” he thought. But like Bumgardner, many seem delighted in the puzzle of emergent orange itself—solution or not. “Even if I can't crack the case on emergent orange,” said Craig Kaplan, “the pursuit affords me the opportunity to produce new artworks in this beautiful medium.”

Bumgardner and his friends are still testing new ideas. It’s like an endless Internet scavenger hunt. As Bumgardner explained by email, “I sometimes wonder if some chemist is going to look at the result and say ‘Well doh, everyone knows that... and point me to page 3 in a textbook on spectrography.’”

And who knows, maybe someday that will happen. But for now, simply having this puzzle—wonderment intact—is as satisfying as decoding it.