The puzzle game genre of “creating shapes from formulas” is currently led by a single designer. Five years after his last sensational hit in the genre, Iranian-born game creator Mahdi Bahrami is back with an even more awe-inspiring – and sometimes hair-pulling – masterpiece.
Whilea new Windows/Mac/Linux game released this week on both Steam and like a direct purchase without DRM for $15 (temporarily on sale for $13.49), is arguably the coolest execution of high-level math I’ve ever seen in a video game. Even better, his challenge is disguised as a handyman. Hand this to any budding young mathematician and watch them get hooked on what is ultimately a brilliant gem of edutainment in disguise.
Axes and allies
The beauty of While comes from the way it turns formula manipulation of the X, Y, and Z axes into a game mechanic. Typical teaching about math formulas involves plotting the results of the solutions on a 2D grid to see what shapes they generate. That’s good enough, although it requires the mathematical calculation of a formula itself. But what if you could do this stuff much faster, and in 3D, by dragging shapes across a series of easily understandable grids, then watching them morph into fantastical new shapes in response?
In each While puzzle, players are given a single geometric shape (sometimes with full 3D properties, sometimes as a flat 2D polygon), and then see the puzzle solution, which is a different geometric shape. Let’s start with a simple example. In the first puzzle of the game, your starting shape (which you can take) is a quarter of the area of the “solution” block (which you cannot touch).
Pick up the shape with your mouse, then place it on a grid of black and white squares. To the right of it, a new shape appears on a grid of bigger black and white squares, and the resulting shape is twice as large on all axes, which coincidentally is the size of the black and white squares on the right side. (Mathematically, it’s a simple multiplication of the values of all the axes.) You can choose either shape, and at this point the larger one fits the solution shape perfectly. Pick it up and move it to a podium next to the solution and While will analyze your submission to confirm that its size, shape and curves are close enough.
The next puzzle indicates how hairy While will eventually become. Its left grid is made up of black and white squares, while the other grid is full of curvy lines. Put a shape at right angles to the left grid, and it will come out of the right grid with its X and Y axes in an equally curvy shape. (Mathematically, here we are looking at a parabolic equation applied to a single axis.)
From now on, While only gets more intense, and its challenging potential is perhaps best summed up by the below collection of shape manipulation GIFs, directed by Bahrami.
If a puzzle has multiple grids on its table, you can put a shape on one of them to generate manipulated shapes on the other grids. Use YOUR MOUSE to lift one of these new shapes, then drag it to another grid for recursive formula application. If a grid turns a 2D shape into a 3D donut, you can grab the resulting donut, move it over the donut grid, and warp it that much more accordingly. The exact placement of 3D shapes on the more intense grids also changes which parts of their shapes are manipulated.