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Is it true that no two snowflakes are alike?

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Up in the winter sky, water vapor in a cloud condenses into a droplet and freezes into a tiny bit of ice, with the water molecules bonding together as a hexagonal crystalline lattice with a six-fold symmetry. As water vapor condenses on its surfaces, the ice crystal grows into a hexagonal prism. As the crystal gets larger and larger, branches begin to form at the corners of the hexagon. When the crystal is heavy enough, it falls through the atmosphere toward the ground, where we call it a snowflake.

Many of those snowflakes have fallen onto the small town of Jericho, Vermont, the home of Wilson Alwyn Bentley. As a teenager, Bentley became interested in snowflakes, and he attempted to draw them while looking at them through a microscope his mother had given him. He found that he couldn't get the complex structures of the flakes down on paper before they melted, so he attached a camera to a microscope using an adjustable bellows mechanism and photographed his first snowflake on January 15, 1885.

Over the next few decades, Bentley continued to study snowflakes, taking 5,381 photographs of them and developing a system to categorize over 80 different flake types and shapes. In 1920, he became a Fellow of the American Meteorological Society and was awarded the Society's first research grant ($25). Bentley sometimes told people that he had never seen two snowflakes that looked alike and published several magazine articles arguing that no two flakes are identical. That idea stuck in the public imagination, which brings us to today's question: was he right?

Scientists have discovered that as an ice crystal gets blown around in the air while it grows, the environmental conditions it is exposed to and the timing of the exposure determine the shape of the snowflake. With different factors determining the snowflake's shape, and that shape changing as the growing snowflake moves through different conditions, you get a lot of variety in snowflake shape. Here's a handy little graph from a Caltech physics professor that shows which shapes occur in which conditions:

cal-tech-snowflakes.jpg

If two growing snowflakes are exposed to the same temperatures and humidity and water saturation levels at the exact same time (live out the exact same lives, if you will), they may look exactly alike at the macroscopic level. In fact, in 1988, the Nancy Knight was studying snowflakes as part of her work with the National Center for Atmospheric Research and found two identical snowflakes of the hollow column type in a Wisconsin snowstorm.

But Caltech physics professor and snowflake expert Kenneth Libbrecht (the man who made the above graph) points out that if you look at any two flakes "“ even seemingly identical ones "“ on the atomic level, you'll find numbers of water molecules and different layouts of those molecules (most water molecules contain an oxygen atom of 16O, but one molecule in every 500 has an 18O). One thing you won't find? Two snowflakes that are exactly alike.

If you've got a burning question that you'd like to see answered here, shoot me an email at flossymatt (at) gmail.com. Twitter users can also make nice with me and ask me questions there. Be sure to give me your name and location (and a link, if you want) so I can give you a little shout out.

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iStock // Ekaterina Minaeva
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Man Buys Two Metric Tons of LEGO Bricks; Sorts Them Via Machine Learning
May 21, 2017
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iStock // Ekaterina Minaeva

Jacques Mattheij made a small, but awesome, mistake. He went on eBay one evening and bid on a bunch of bulk LEGO brick auctions, then went to sleep. Upon waking, he discovered that he was the high bidder on many, and was now the proud owner of two tons of LEGO bricks. (This is about 4400 pounds.) He wrote, "[L]esson 1: if you win almost all bids you are bidding too high."

Mattheij had noticed that bulk, unsorted bricks sell for something like €10/kilogram, whereas sets are roughly €40/kg and rare parts go for up to €100/kg. Much of the value of the bricks is in their sorting. If he could reduce the entropy of these bins of unsorted bricks, he could make a tidy profit. While many people do this work by hand, the problem is enormous—just the kind of challenge for a computer. Mattheij writes:

There are 38000+ shapes and there are 100+ possible shades of color (you can roughly tell how old someone is by asking them what lego colors they remember from their youth).

In the following months, Mattheij built a proof-of-concept sorting system using, of course, LEGO. He broke the problem down into a series of sub-problems (including "feeding LEGO reliably from a hopper is surprisingly hard," one of those facts of nature that will stymie even the best system design). After tinkering with the prototype at length, he expanded the system to a surprisingly complex system of conveyer belts (powered by a home treadmill), various pieces of cabinetry, and "copious quantities of crazy glue."

Here's a video showing the current system running at low speed:

The key part of the system was running the bricks past a camera paired with a computer running a neural net-based image classifier. That allows the computer (when sufficiently trained on brick images) to recognize bricks and thus categorize them by color, shape, or other parameters. Remember that as bricks pass by, they can be in any orientation, can be dirty, can even be stuck to other pieces. So having a flexible software system is key to recognizing—in a fraction of a second—what a given brick is, in order to sort it out. When a match is found, a jet of compressed air pops the piece off the conveyer belt and into a waiting bin.

After much experimentation, Mattheij rewrote the software (several times in fact) to accomplish a variety of basic tasks. At its core, the system takes images from a webcam and feeds them to a neural network to do the classification. Of course, the neural net needs to be "trained" by showing it lots of images, and telling it what those images represent. Mattheij's breakthrough was allowing the machine to effectively train itself, with guidance: Running pieces through allows the system to take its own photos, make a guess, and build on that guess. As long as Mattheij corrects the incorrect guesses, he ends up with a decent (and self-reinforcing) corpus of training data. As the machine continues running, it can rack up more training, allowing it to recognize a broad variety of pieces on the fly.

Here's another video, focusing on how the pieces move on conveyer belts (running at slow speed so puny humans can follow). You can also see the air jets in action:

In an email interview, Mattheij told Mental Floss that the system currently sorts LEGO bricks into more than 50 categories. It can also be run in a color-sorting mode to bin the parts across 12 color groups. (Thus at present you'd likely do a two-pass sort on the bricks: once for shape, then a separate pass for color.) He continues to refine the system, with a focus on making its recognition abilities faster. At some point down the line, he plans to make the software portion open source. You're on your own as far as building conveyer belts, bins, and so forth.

Check out Mattheij's writeup in two parts for more information. It starts with an overview of the story, followed up with a deep dive on the software. He's also tweeting about the project (among other things). And if you look around a bit, you'll find bulk LEGO brick auctions online—it's definitely a thing!

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Name the Author Based on the Character
May 23, 2017
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