The Make Shapes From Formulas puzzle game genre is currently ruled by a single designer. Five years after his last sensational foray into the genre, Iranian-born games maker Mahdi Bahrami has returned with an even more impressive – and at times outrageously difficult – enigmatic masterpiece.
Tandisout this week on both steam and how a direct, DRM-free purchase for $15 (temporarily on sale for $13.49) is arguably the coolest execution of high-level math I’ve ever seen in a PC game. Even better, his challenge is disguised as a craft toy. Hand this to any young, aspiring mathematician and watch them become addicted to what ultimately is a brilliant edutainment gem in disguise.
Axes and Allies
The beauty of Tandis comes from how it turns the formulaic manipulation of X, Y, and Z axes into a game mechanic. Typical teaching of mathematical formulas revolves around plotting solution results on a 2D grid to see what shapes they produce. That’s fine – although it does require the mathematical grokking of a formula itself. But what if you could do something like this much faster and in 3D, by dragging shapes onto an easy-to-understand series of grids and then watching them morph into awesome new shapes in response?
In each Tandis Puzzles give players a single geometric shape (sometimes with full 3D properties, sometimes as a flat 2D polygon), then they are shown the solution to the puzzle, 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 pick up) is a quarter the volume of the “solution” block (which you can’t touch).
Pick up the shape with your mouse, then place it on a grid of black and white squares. To the right of this, a new shape appears on a grid of greater Black and white squares, and the resulting shape is twice the size on all axes – which is random enough given how much larger the black and white squares on the right are. (Mathematically, that’s a simple multiplication of the values of all the axes.) You can choose any shape, and at this point, the larger one fits the solution shape perfectly. Pick it up and place it on a pedestal next to the solution and Tandis will scan your template to confirm the size, shape and curves are close enough.
The next riddle suggests how hairy Tandis will eventually become. The grid on the left consists of black and white squares, while the other grid is full of squiggly lines. If you put a rectangular shape on the left grid, it will come out of the right grid with its X and Y axes evenly squiggled. (Mathematically, here we are considering a parabolic equation applied to a single axis.)
From here, Tandis only gets more intense, and its challenge potential is perhaps best summed up by the collection below of shape manipulation GIFs as created by Bahrami.
If a puzzle has multiple grids on its table, you can place a shape on one of them to create manipulated shapes on the other grids. Use your mouse to lift one of these new shapes, then move it to another grid for recursive formula application. When a grid converts a 2D shape into a 3D donut, you can grab the resulting donut and move it onto the donutization grid, distorting it even more. The precise placement of 3D shapes on the more intense grids further changes which parts of their shapes are manipulated.
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