Bismuth Crystal Puzzle and the Matrix Cut

The Bismuth Crystal Puzzle is the successor to our popular Geode and Agate puzzles; the next in our growing line of unique geological puzzles. It is a one-of-a-kind jigsaw puzzle inspired by the remarkable geometric patterns found in bismuth crystals. Each puzzle is uniquely generated through a computer simulation, mimicking natural variations in shape and design. It features a new cut style we’re calling Matrix, a geometric cut reflecting the puzzle’s crystalline nature. There are two sizes available in our shop now: the Bismuth Crystal Puzzle ($60, ~157 pieces) and the Big Bismuth Crystal Puzzle ($85, ~267 pieces).

The puzzle artwork is inspired by the distinctive structures created by bismuth’s “hopper growth.” Imagine a set of miniature, interconnected staircases or terraces, each stacked upon the other, creating a surreal, layered landscape. The images are grown in a simulation we created inspired by bismuth and are available in five vibrant color schemes. Each image starts from one or more seeds with a different orientation or in crystallographic terms a “grain”. The layers grow as a simple offset from the previous layer. As they interact with each other and their environment, defects form, generating kaleidoscopic spirals of vibrant color.

Puzzle Cut style – Matrix

These puzzles have a new geometric cut inspired by the puzzle’s crystalline nature. The Matrix cut is our take on a grid based puzzle style. However, this grid flows and conforms to a changing direction field which matches the puzzle border. We wanted a cut that would match the rhombohedral symmetry of the bismuth crystal while also accentuating each puzzle’s unique shape. The Matrix cut is now available in the Custom Puzzle maker and works especially well with custom shaped puzzles, as the grid warps to the puzzle’s boundary.

The cuts are generated by first creating a roughly equilateral quad mesh based on the puzzle shape. The directionality of the quad mesh is determined by the boundary, the whimsy pieces, and additional curves that we can introduce as design elements to undermine the rigid structure of the grid. We seed this grid with pieces that are made of roughly equal numbers of quadrilaterals with no gaps in between them. The pieces then undergo an optimization process where neighboring pieces can exchange faces. The edges between pieces are scored by how interlocked the pieces are. This interlocking is measured by looking at the kind of “Gauss map” of the curve of an edge. That is how much of a circle is covered by looking at the tangents of the curve. Over 180 degrees will ensure some amount of interlocking, while 360 will be very interlocked. The optimization process makes sure the play of the puzzle is satisfyingly tight while also generating intriguing, irregular piece shapes.

Puzzle details

The puzzle comes in two varieties. The regular Bismuth Crystal Puzzle comes blind-boxed; pick from one of our 5 colorways and you will receive a surprising design unique to you. Don’t worry, the puzzles come with an image of the one-of-a-kind design which you can use (or not if you want an extra challenge) to aid in the assembly. Each one has approximately 157 pieces and is about 9 inches square, however, due to the puzzles unique nature, the exact size and number of pieces will vary. The Big Bismuth Crystal puzzle is a larger variety, and it is available in limited choose your own designs just like our Agate puzzles. We will regularly list new ones, so if your desired color runs out, check back later for more. These larger puzzles are about 11 inches and have about 267 pieces.

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