Braided Galton Boards – Visualizing Probabilities with String

I’ve been playing around with Galton Boards recently. They’re an awesome demonstration of the central limit theorem, and how several independent 50/50 events sum together to make a Gaussian/Bell curve.

Seeing the standard Galton board gives an intuitive feel for how random variables behave, but it takes time to run the experiment and see the results accumulate.

I wanted a more immediate visual demonstration, and after a few prototypes I settled on using a thread to represent each possible path through the system:


I used 12.5mm dowels cut to size, and hammered into the lasercut wood.


The 64 and 32 string versions

The strings are cut to length, then held in place with a screw clamp and threaded through one at a time:


Stats and craft therapy all in one

It might be because I finished this late at night, but I found it very difficult to thread without making a mistake. The strategy I ended up using was to hold the previous thread in my left hand and the next thread in my right. By jiggling my left hand I saw the old thread bounce, which gave a good reminder of where I was in the sequence, and hence to put the new thread in the right spot.


Files here for anyone that wants to make their own:

It took a bit of prototyping before I got a form factor I was happy with. Here’s two of the failed attempts, that I avoided because they either weren’t practical, or they were slightly too opaque a display of the concept:


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Lasercut Yarn Bobbins

I’m working on a project that involves lots of different coloured cords, and I wanted a way to avoid tangles while transporting & working with them.


Files here:


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Bayes’ Ruler – A Bayesian Slide Rule

I’m a big fan of Bayesian statistics, and also old analog computers. It occured to me one day that I hadn’t ever seen a slide rule for calculating Bayes’ theorem…


Behold a fine posterior

Here’s how to use it. Let’s say you’re a doctor, and treating a patient with a 80% chance of having gallstones. You order a new test done, and it comes back positive. What’s the probability they have gallstones?

After looking in the medical texts, you find the test is 5:1 more likely to be positive if the person has gallstones than if they don’t.

So, we align the arrow with our ‘prior’ on the left at 80% (4:1 odds), and look for the 5:1 diagnostic odds, which gives us a result of 20:1, or 95.2% probable the patient has gallstones.


There’s far better explanations out there than this, please check out Wikipedia for what’s almost certainly better worded than mine.

I didn’t have the heart to design something like this by hand in inkscape. Instead I used Python and the DXFwrite library  to generate the files, and then lasercut it from acrylic.


I also made a wooden version with a clear acrylic top, which should be less fragile in a bag:



Files are here for anyone that wants to make their own:


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Pachinko Crystal Modelling

I saw this video recently, and fell in love with the Atomix toy. Sadly it seems you can’t get them anymore. However, I remembered that in the garage  I had over a thousand Japanese pachinko balls left over from a previous project…

This was a quick one evening build, I just wanted to get it done before I got distracted. Some sawing and cutting later, and here’s what I have:


Can for scale, as with all my projects

I used thick 12mm thick plywood I had laying around the space, and a bandsaw-box like technique to cut out the inside of the frame. The front is lasercut 3mm acrylic, which I was originally worried might not be up to the job of keeping 3kg of agitated steel contained, but after shaking it a few times it seems to be sturdy enough.

You can hold the frame and shake it by hand, but I wanted something to be a bit more play-friendly. I had a lazy-susan bearing kicking around after I did various rebuilds of  a robot several years ago, and I decided that would allow some gentle motion.


4×2 lovingly cut, and expertly screwed together in whatever fashion got it done before bedtime. 

With two wood pieces acting as a tilted base, the whole assembly sits tilted on the table and can be gently rotated with a light touch.

Tilted base.jpg

Finished piece

It’s certainly very  satisfying to play around with, you can see the fault lines, grain boundaries, different orientations, gaps and other nifty crystallographic features. And for a one evening build I’m very happy with it.

Also, words can’t express how noisy the 11mm pachinko balls are compared to the ~1mm ones Steve used in his model. However provided you’re the one using it, it’s relaxing and soothing like a rain machine. (However if someone else is doing the playing, for some reason it doesn’t seem quite so serene…)

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Demonstration ROS Coordinate Frames

I spent a bit of time recently help a friend set up a robotics lab. One of the things I wanted to nail down was a consistent set of coordinate frames for all the equipment.

The Robot Operating System is awesome, and provided you set up your TF models correctly, it’ll do all the work for you. However it’s sometimes counterintuitive how it should be set up. ROS has a standard way of arranging coordinates (REP0103), but it’s different for ordinary coordinate frames and camera frames. (For very good historical reasons; the camera frame has Z pointing forwards, which means X is lined up with image columns, and Y is image rows).

I decided to make some tangible models for people to use when they’re discussing transformations. When troubleshooting robots you constantly find yourself in front of a whiteboard making “finger axes”, I wanted something we could use instead, and that had the same colouring and labels as the software.

The idea is first, to have something tangible to play with while brainstorming, and second, as a reminder of the convention, to allow errors to be detected. If there’s an error, I really want someone to ask “Wait, why is the green arrow pointing in a different direction on screen?”.


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Making the ‘Ultimate’ Pochade Boxes

The previous  writeup was getting a bit long, so I thought I’d put the steps used for making the boxes in their own post.


I started with the frame, using pine and biscuit joints for securing it:


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The ‘Ultimate’ Pochade Box

I’ve been getting interested in plein air oil painting recently, not so coincidentally after Netflix brought out some inspiration.

As with any set of tools, painting equipment only has value if you actually use it, and lots of hobbies get dropped, not because people don’t enjoy them, but because it’s slightly too hard to use regularly. Adam Savage has a great saying, that “drawers are where tools go to die”, i.e. if it’s out of sight, we forget it’s there, and we’re not motivated to look for it.

Hence, I wanted to make sure I had a way to make it easy to get painting. To make getting going on any given day require the absolute bare minimum of ‘spritual energy’, gumption, spoons or other resources that might be running low.

Enter the pochade box! Pochades (from the French for pocket) are an all-in-one way of carrying around supplies and a way of working on paintings in the field.

My wishlist of features was something like this:

  • Must allow stopping and starting just by opening & closing the box
    • No pack up time, fussing to turn canvases around, add clips, put them in separate boxes for transport.
  • Must allow carrying of essentials & tools:
    • Paints, brushes, small amount of solvent & mediums, pencils, etc
    • The two exceptions to this are a roll of paper towels, and the (leakproof) brush washer tin, which I’m happy to carry in my backpack.
  • Tools should be exposed for easy use during painting.
    • This was my major peeve with the French easel design, by hiding stuff behind the canvas, I’m likely to forget it’s there, or be too lazy to use it when I should.
  • Wet canvas carrier
    • Utterly essential. Nothing’s going to add stress to the end of the day like manouvering a wet canvas around safely.
  • Multiple sizes of canvas able to be carried
    • Many pochade boxes are single size only, and lots of artists end up owning three or four different sized boxes, no joke. Of course having a separate small box is much lighter for quick trips, but still flexibility is handy.
  • Should sit flat on a desk, and not take up too much room if I’m sharing a desk with others
    • This one is more a response to some French easel style pochade boxes I saw. They claim to fold up the tripod legs and allow you to use it on a desk in a class environment. It might be just me, but if I’m indoors with a group, I’d feel extremely self conscious having a huge folded tripod on the desk.
  • Weight goal: Hmm… ‘Luggable‘.
    • Lightweight would be good, but I’m aiming for something I can carry a few hundred meters from a car, rather than something you can climb a mountain with.
  • Glass palette as mixing surface
    • Easy cleanup, also allows putting reference material underneath
    • Should be removable, as it allows storing unused paint in the freezer

I took my time playing around with ideas for this one. After more than a week of sketching and researching other people’s designs, I had some idea of what I wanted to do.

This is the final result. (Why are there two? At some point through construction, I realised I’d put enough safety margin in my wood purchase to make a whole other box, and I couldn’t resist having a matched set).



Here’s what I came up with for wet canvas storage, it’s adjustable to any size canvas, and you can have a pair of different sized wet canvases in place without them touching:


I was inspired by this pochade from Ruth Vines, but modified it so the rods don’t extend out of the box.

The boards are held in place by plastic extrusion used for sliding cupboard doors. The wooden pieces have ‘U’ cutouts and can be completely removed by loosening the nuts and just sliding the frame out. The lower frame has a cutout allowing taller canvasses to pass through:


Both of the box sides have a pullout work surface, something to rest brushes, solvent containers and other miscellaneous bits on:


I might add in some cutouts to act as brush or tool holders

The glass palette surface was just a $5 A4 photo frame screwed to the surface. This has the added bonus that I can put a printed sheet underneath to help me get consistent palette ordering, and a value scale to compare against while painting:


For some reason the hackerspace printer was making the greyscales at the bottom green?  Meh, I’ll fix it later

And of course the palette can be removed & stored in the freezer (to keep the paints wet as long as possible)


The final thing to do was add something to differentiate the two boxes, so I can grab the right one in a hurry. Using the obligatory naming convention I made a couple of lasercut labels:


And on the box:


Albrecht and Balthasar ready for action

Sometime I’ll probably put a polyurethane coating on for protection, but they’re pretty sturdy.

I’ve had a chance to carry them around a bit now, and while they’re not light, they’re acceptably ‘luggable’, and I can carry one a kilometer or two without major injuries. They’ve also proved more than sturdy enough to use as a seat while waiting for a train!

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