maths

9 Articles

Procedurally Generating Marble Runs

March 4, 2020 by 7 Comments

Marble runs are somehow incredibly soothing to play with and watch, with the gentle clack of the marbles and the smooth, predictable motion. Sadly for some, they never quite got enough time to enjoy them in school. Luckily, [Fernando Jerez] is here with a way to procedurally generate marble runs you can actually play with!

[Fernando] does a great job of explaining the mathematical process of generating the marble runs, using the method of random space filling curves. A maze is drawn on a grid, with points on the grid acting as walls. Each grid cell is then given a value based on points on its corners, and these values then translate into directions of travel. This creates a path through the maze. Scaling this path along the Z-axis, and then replacing the path with a marble track creates the run. It’s then a simple matter of adding a shaft to the loop with a screw to drive marbles back to the top of the run, and you’re all set!

With both animated explanations and actual 3D printed marble runs, [Fernando] demonstrates the concept well. We’d love to print a few runs of our own, and we can’t help but think there’s other great applications for the mathematics behind this concept. If you’re wise to it, drop it in the comments. Otherwise, check out these exquisite creations we’ve featured before!

Simulating Snakes And Ladders For Fun, Not Profit

July 23, 2017 by 11 Comments

A great many of you will remember the game of Snakes and Ladders from your youth. It’s a simple game, which one grows to realise involves absolutely no skill – it’s purely the luck of the dice. [Alex Laratro] noticed that without player decisions to effect the outcome, the game was thus a prime candidate for simulation. 

[Alex] wanted to dive into the question of “Who is winning a game of Snakes and Ladders?” at any given point in the gameplay. A common approach would be to state “whoever is in front”, but the ladders might have something to say about that. [Alex] uses Markov analysis to investigate, coming to some interesting conclusions about how the game works, and how this compares to the design of more complex games like Mario Kart and Power Grid.

Overall, it’s a breakdown of a popular game that’s simple enough to really sink your teeth into, but has some incredibly interesting conclusions that are well worth considering for anyone designing their own board games. We love seeing math applied to novel and fun problems – and it can solve important problems, too.