Well, it happened again: I saw a new science paper that sounded interesting, started reading, and fell down a rabbit hole. The subject this time? Fractals.
It all started with this press release I found out of the University of Oregon, discussing a new paper from UO physicist Richard Taylor. He and his team
“examined the question: “What happens in your brain when you walk down the street?” and they concluded that urban environments are not pleasing to the human brain.”
Well sure, that’s understandable! After all, urban environments can be loud, they can smell bad, they can remind us of work, they can be crowded, the air can be polluted. So why, exactly, did Taylor’s team find people preferred a walk in the woods to a walk in the city?
“The reason is the lack of fractals in modern architecture and spaces. Fractals are patterns that self-repeat at different scales, and they can be found all over nature in objects like trees, rivers, clouds and coastlines.”
Okay, that was NOT where I thought that was going.
There’s been loads and loads of research showing that people experience less stress when they’re in or around or able to look at green spaces. There’s something about trees and nature that make us calm down and feel better. I’ve talked about some of those studies here in the past – they’re pretty convincing. “Touch grass” isn’t just an insult to get someone to rage quit a video game, it’s a scientifically proven technique to improve their attitude.
But fractals? That was new to me. I know what fractals are, more or less from a layperson’s viewpoint: they are self-repeating, self-similar sets; geometric patterns that don’t change the further you zoom in or out. They ARE found often in nature, with some common examples being the way a bolt of lightning forks, the way trees branch, or even the way cauliflower grows. While philosophers and mathematicians have theorized on them for hundreds of years, it wasn’t until Benoit Mandelbrot wrapped the idea up in the word “fractal” that they really took off both in research and in the public consciousness.
It’s no coincidence that that happened at the same time that the computer started taking off, because computing software gave people the ability to fairly easily create their own digital fractals.
But what’s this got to do with people enjoying being in nature versus a city street? The press release states:
““As soon as we look at nature, it triggers a cascade of automatic responses,” Taylor explained. “Even before we’ve noticed what we’re looking at, we’re responding to it.”
And the response is a positive one. Humans experience less stress and better well-being when looking at nature, and this is driven by fractals. Taylor’s research has found that fractals can reduce stress and mental fatigue for the observer by as much as 60 percent.
Taylor also points to research that showed hospitalized patients could heal faster when they had access to a window because looking outside, and at all of the natural fractals. helped patients relax their bodies and heal faster.”
Taylor says modern architecture doesn’t incorporate fractals, and that makes us sad. Huh!
I was very interested in how he and his team went about proving this, because it’s rather complicated: first, you have someone’s subjective experience of enjoyment of a walk, which can be affected by hundreds of things from what they had to breakfast that day to whether or not it’s supposed to rain on Saturday.
Once you’re able to fairly compare a walk in the woods to a walk in the city, you’d need to control for all those things that scientists already know make people feel better when they’re in nature: the fresh air over polluted air, the sound of leaves over the sound of traffic, the lack of company over the crush of a crowd, the greens and blues over the greys and greys.
Finally, once you are able to control for all of that, how do you manage to identify “fractals” as the remaining happiness factor?
To answer those questions, I sought out the actual paper, which was difficult because the press release didn’t bother to link to it. I found it published in this month’s issue of Urban Science: “What Happens in Your Brain When You Walk Down the Street? Implications of Architectural Proportions, Biophilia, and Fractal Geometry for Urban Science.”
That paper is about a thousand pages long. Okay, no, it’s 35 pages long but I just got back from a weeklong vacation and my brain is fried from mai tais, sunshine, time zone changes, and Daylight Savings Time, so give me a break. But I read it all in case you don’t want to, so let me start by saying this: this paper is not about an experiment. They didn’t take a bunch of subjects and make them walk down a city street or through a forest while wearing a portable functional MRI machine and eye tracking goggles, though that would have been dope. No, this paper is actually a summary of about a hundred previous papers, assembled in such a way as to make the argument that you prefer to walk in a forest rather than a city street because of fractals. So if you think about it, this is not a meta-analysis but it IS a scientific paper about other scientific papers, which is in itself recursive. This is a fractal paper. Mind blown. (Thanks to my friend Joe for giving me that joke.)
And I gotta say, I went in VERY skeptical but they do make some good points. To reach the conclusion that “we prefer nature to cities because we like fractals,” they support several points:
1.) That looking at fractals makes people happy.
2.) That fractals are UNIVERSALLY considered “beautiful” regardless of cultural upbringing or mood
3.) That “modern” urban architecture is severely lacking in the use of fractals, which means
4.) we get more stressed out on a modern city street than in a forest.
The evidence for #1, that looking at fractals is a nice experience, is pretty good. Unfortunately the press release conflates a few things mentioned in the paper: for instance, they write “Taylor also points to research that showed hospitalized patients could heal faster when they had access to a window because looking outside, and at all of the natural fractals. helped patients relax their bodies and heal faster.” But those studies didn’t mention “fractals.” It was just showing patients “natural” versus “urban” environments to see who improved the fastest. I couldn’t find any evidence referenced in this paper that says FRACTALS in and of themselves have magical healing properties.
But sure, there are studies referenced like “Universal aesthetic of fractals” that found preliminary evidence that people preferred looking at fractals that were more “fractally” (my word). But that leads me directly into #2: are fractals really “universally” beautiful? The title of that paper suggests it is, but in fact the experiment only covered exactly the people who are always covered in these papers: 220 undergraduate college students.
Every referenced study I clicked on was the same, and every one still talked about “universality” of preference for fractals, but okay, sure. Even those studies found very messy data, like “Quantifying Aesthetic Preference for Chaotic Patterns” (24 subjects from the university) which found “self-reported creative individuals have a marginally greater preference for high F patterns and self-reported scientific individuals preferred high L patterns. Objective tests suggest that creative individuals had a slightly greater preference for patterns with a low F.”
Or then there’s “Aesthetic Responses to Exact Fractals Driven by Physical Complexity” which found no universality among the handful of UO undergrads who looked at exact fractals (the fractalliest). And yeah a LOT of this kind of fractal research is coming out of Taylor’s lab at UO.
I have to pause here to mention that I find it endlessly amusing that all these studies are in effect attempting to prove that the more complicated the pattern, the more it’s worth, like Dan Flashes. Anyway.
Do humans like looking at fractals? Many of us seem to, yes, but not way more than we like looking at other things. Is that slight preference universal? In the dozens of referenced studies I read, it doesn’t seem so, no.
That’s not to say there hasn’t been research done on fractals and people who aren’t Western white university undergrads, which brings me to point number 3 from this paper, that “modern” urban architecture is severely lacking in the use of fractals. I found it interesting that this paper exclusively mentions the “universal” “beauty” of cities built with classical architecture in Europe: Rome, Barcelona, and Lucca, Italy. I started wondering, what about the other 97% of the populated world? Well! Researchers like Ron Eglash have made their living studying fractals in indigenous cultures, pointing out that many African villages are organized in fractals, like this extremely cool village that persists all the way down to a tiny version of the village in each home that is built for spirit ancestors, who presumably have tiny versions in THEIR village.
And admittedly, I saw these fractal villages and thought, “wow, pretty!” I like looking at them. So there’s a data point.
Anyway, Euro-centrism aside, this IS a point where I was won over by compelling evidence: “modernist” architecture does rely less on fractals compared to “classical” architecture (and other styles as well: I’m not sure why this paper is so focused on European classical architecture when surely this would apply to every other architectural trend as well). But the entire point of modernism as popularized by people like Le Corbusier in the 1920s, or at least the primary thrust, was the idea of function over form, of removing extraneous flourishes and distilling the building down to its flat, straight, essence. By relying on large panes of glass, right angles, and stark aesthetics, many modernist buildings DO have less complexity than many examples of classical architecture.
That said, modernism is a big umbrella. I’m no expert, but I did spend a few years writing copy for a construction contractor who worked on historic buildings around New England from modernist icons like I.M. Pei and Le Corb. And yes, Boston has the John Hancock Center, designed as a pristine glass rectangle by Henry Cobb in 1976, but there’s also the Frank Gehry Stata Center that looks like it fell out of a Dr. Seuss book (and here’s some inside info: as fun as the building looks, it’s a real pain in the ass to repair anything that goes wrong and I also heard that the students hated the internal design).
Then you have Boston City Hall, which is often used as an example of brutalism gone wrong. Pretty much no one likes Boston City Hall, likening it to an alien space ship that landed in the middle of a brick desert. It’s unwelcoming, and monstrous, and supposedly failed in incorporating the true purpose of brutalism, which was to contrast large slabs of concrete with surrounding trees and nature, not bricks. But take a look at it, and what do you see? I see…well, now I see fractals. Rectangles in rectangles.
All of this is to say: maybe there’s a bit of cherrypicking going on when we make a blanket assertion that the complexity found in classical architecture is better than that found in modernist, and maybe all of this makes it far too complicated to say “we hate walking in a modern city because there aren’t enough fractals.” While this paper was very interesting and I’d love to see them try to support their hypothesis with experimentation, and while I did come around a bit after some serious early skepticism, it’s just not enough. There are so many big, obvious reasons why many large cities aren’t pleasant to wander around, possibly the most obvious being that they were built for cars to drive around. When you build a city for vehicles, when you skip out on sidewalks and bike lanes and small local shops, you can’t act shocked that people don’t love to walk around it on their feet.
Urban planners already know this, and they know that people enjoy seeing trees and water and the sky, whether that’s due to fractals or not. The problem is that they run up against people who profit off of cars and big box stores with large parking lots next to them, and skyscrapers where people can go to work and then immediately go home to the suburbs.
But despite the lack of evidence that increasing the number of fractals in our cities would improve our lives, this paper stands by that conclusion. Why? I’m sure Richard Taylor is a smart and thoughtful person who is genuinely convinced that fractals will improve the world, but in 2019 he collaborated with designers to produce fractal carpeting to sell to large venues like hotel chains, that he says are scientifically proven to reduce stress. Huh.
And this new paper’s press release proclaims “Taylor is collaborating with UO psychologist Margaret Sereno and architect Ihab Elzeyadi on scientifically informed design projects that incorporate the kind of fractals that are pleasing to the human brain when viewed in the spaces people work and live in. Some examples are the fractal carpets that Taylor’s team designed for the Knight Campus and spaces like workplaces, schools, airports and other places where people experience heightened anxiety.
“That same design concept could be integrated into ceilings, window blinds and other parts of modern architecture, Taylor said. The UO collaborators have another project that develops fractal patterns for rooftop solar panels.
“He points to a college campus as a prime place to prioritize making architecture and design more human-centered. Imagine, he said, if students were able to look at fractals instead of simple boxes and walls on an exam morning. That would automatically reduce their stress and put their minds in a better place for the test.”
I should also note that he previously published a paper claiming to be able to detect art forgeries based on fractal patterns, particularly in regards to the work of Jackson Pollock, for which the Pollock–Krasner Foundation paid him. Also of note is that some other scientists pushed back on this claim: Kate Brown, then of Case Western University, published a rebuttal claiming that she was unable to reproduce Taylor’s results and that her own Pollock forgeries passed his fractal test. In a case of “wow it’s a small world,” her co-author on that paper was none other than physicist Lawrence Krauss, which viewers of this channel may better know as “that physicist who bet his entire livelihood on telling the world he’s not ashamed to say he loves Jeffrey Epstein,” which, well, didn’t work out well for him. That’s got nothing to do with whether or not a guy can tell a real Pollock from a fake one based on the fractals, just a fun coincidence.
All of this is to say that I see a lot of red flags here. A common warning sign that you’re dealing with pseudoscience is when someone says their “cure” can apply to anything, like how many chiropractors think they can fix your back ache, your neck ache, oh and maybe your bowel cancer, too. Fractals are invoked not just in nature, in art, and in architecture, but also in James Joyce’s Finnegan’s Wake, in the stock market (as argued by Benoit Mandelbrot himself), and even in the evolution of cities themselves. It doesn’t mean those things aren’t true – it just means that there’s a big barrier to overcome to prove it is true. And when it comes to arguing that something is fractal, say in the case of the stock market, you can always argue that 1) it’s not an EXACT repeating pattern, just a similar one, and 2) that you haven’t zoomed out enough to see the full pattern. Humans are remarkably good at finding patterns in things, even when there is no pattern to find. While fractals are a mathematical necessity at this point, and while they’re fascinating to look at and play with and consider, we need a lot more empirical evidence before we can say that the patterns we see all around us are truly fractals, let alone whether they are intentional (when made by humans) or beneficial (when found in art and architecture).