Math Games

the problem is that it started as a deathmatch level and it has no structure at all haha

never thought of making it into a puzzle though, shit, now i gotta…think some more…

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yeah a puzzle can just be walking and opening doors. you can make a maze interesting by simply making the space puzzling to traverse.

or just make a really cool doom level

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Yeah one of my most popular levels in Mario Maker 1 was basically just a pipe maze. Heck, my screen wrapping puzzle in MM2 was mostly a maze too. Navigating complicated spaces is pretty engaging!

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are there any games that explore projective geometry?

I recall seeing a trailer for a first person game where you picked up an object, held it in front of you and then the object became part of the level geometry you could move through. One part showed the player picking up a photograph of a hallway, holding it at arms length in front of a blank wall then after fixing it in place being able to walk forward into the hallway in the photograph.

I think you actually had a camera and were taking the pictures yourself. You could photograph anything and then walk into the photo at will. And you could set it at any weird angle too so when you went into it the geometry would be all skewed.

I was going to include in my initial post but could never remember the name of it.

I guess that’s using projective geometry?

That ought to be Superliminal or its predecessor student game. Similarly, Perspective is about 2D constructions of 3D scenes (the narrative hints at higher-dimension representations but it’s not illustrated in gameplay)

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it’s using perspective projection! but then again so are nearly all 3d games

projective geometry is sort of a rigorous interpretation of the “vanishing points” you get in perspective projection, a.k.a. “points at infinity”, which are said to all lie on the “line at infinity” (or horizon). incorporating these concepts into regular plane geometry introduces strange & intriguing features such as the logical symmetry of lines and points (any two points lie on a specific line; any two lines intersect at a specific point), or how crossing the horizon flips you over to a mirror image of the same space, or how all the conic sections can be understood in this setting as different views of the same shape

e.g. parabola ~ ellipse

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@Mr_Mechanical I think this is the one you were thinking of

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Yeah I was going to ask if you were making a joke at first lol.

@Mikey Yeah I think that’s the one!

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https://twitter.com/mattstark256

Development continues, per the dev’s Twitter account

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ah

there are definitely games that play with the difference between orthographic projection and perspective projection to reveal information (an idea that spontaneously generates every few years because the matrix math suggests it, and 3D editors always have a toggle), but I can’t think of any that render world collision based off it

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4D Maze Game

It is difficult to display a three-dimensional set of colors on a two-dimensional computer screen, so I decided to consider black to be transparent and arrange for most of the world to be black. That reduced the original solid block of color to a set of three-dimensional lines. Then I created a three-dimensional vector display using stereo pairs of images.


Hello everyone, it’s Pacman 5d

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in the vein of Marble Marcher:

fractals as cosmic horror

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Founding statement for this Oddity:

“The Ultimate Display”, Ivan Sutherland, 1965. Whitepaper speculating on the use of future displays and input devices to intuitively grasp mathematical realities:

We live in a physical world whose properties we have come to know well through long familiarity. […] We lack corresponding familiarity with the forces on charged particles, forces in non-uniform fields, the effects of nonprojective geometric transformations, and high-inertia, low friction motion. A display connected to a digital computer gives us a chance to gain familiarity with concepts not realizable in the physical world. It is a looking glass into a mathematical wonderland.

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Found a hyperbolic sokoban playable in a browser. Neat!

EDIT: ah everything is so far away! lol

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This is chill, not as much fussing around as I’d expect there to be. It seems like the use of corridors are what make some of these levels feel so big, pinpointing open spaces to reorient the crescent blocks is pretty satisfying though

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Surprised how similar it feels to HyperRogue despite HyperRogue using a hexagon/heptagon tessellation, and this only being “squares”.

It’s harder to get a sense about how rotation works on a hexagonal grid, but on the square one it’s really obvious because 5 right turns makes you end up in the same space but an obviously different orientation.

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this makes me wonder how the level data is organized and generated

like, use a 3D modeler and input the vertices?

The about page mentions some pretty mathy shit, so I’d guess it’s closer to a loose connection of points or coordinates rather than a continuous data structure, yeah. Sounds like they’re converting between coordinate systems to render it then, too.

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