Mechanic suggestions from AWESOME MATHEMATICS

Private: Forums Suggestions Mechanic suggestions from AWESOME MATHEMATICS

This topic contains 3 replies, has 2 voices, and was last updated by  Biological_topologist 2 years, 6 months ago.

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  • #219

    Yo. So I tweeted some of this to Logan a while ago, but I thought I might put something down here to make it clearer, or maybe check on the status to see if there was any experimentation?

    To a topologist, Four Sided Fantasy is about experimenting with a donut. In the biz we call them TORUSES!
    Just need to clarify this first before we move onto new stuff. When you hold the button in four sided fantasy, it becomes the case that the top edge of the screen is connected to the bottom and the left to the right – right? Soo, watch this
    wrap up
    I suspect that we ARE all aware of this, because there was a gif of a torus on the kickstarter page:
    Four Sided Fantasy Puzzles www foursidedfantas
    And hey, look at that, there are multiple copies the screen on the torus. You could have any number of copies on there and the concept would still be consistent
    torus<br />upload pictures free<br /><br />

    Oh dear god what a horrible illustration of the beauty of this game, please don’t let the press see this. I’m just showing you coz I need to establish a style that Im gonna continue using.

    Starting “easy”: Four sided fantasy on the surface of a sphere
    CHECK THIS OUT:
    1280px Peirce quincuncial projection SW<br />photo hosting sites<br /><br />
    Is that a map of the world? Why yes, yes it is. And what shape is the world? No wait, first, is the world donut-shaped? No, no it isn’t, that would be weird. FSF, currently IS donut shaped, so we have to be looking at something different here. SPECIFICALLY: The world is a ball. Therefore, that picture above is a picture of a ball.

    Do me a favour: stare at that map for a while, and imagine being a boat sailing through its briny sea. What would happen to you if you went off an edge, say you go down the bottom left, bearing south east from south america – what would happen? Well obv, if you sail south east from south america you get to south Africa. Soooo, on this map you go through the bottom edge and come straight back out of it, but on the right. Here’s another horrible picture:

    So yeah, could experiment with that mechanic? Im just gonna tell you: this shit is important in mathematics. We’ll get to that at the end maybe though.

    A bit more fun: mobius strip
    You get a mobius strip by taking a strip of paper and joining its ends together with a single little twist.
    strip<br />free image upload<br /><br />

    Maybe you can already see how this would relate to FSF. Need to tell you this about mobius strips though: They have a strong link to “reflection”. This will show you why: https://www.youtube.com/watch?v=4mdEsouIXGM

    If you want to do a proper topological mobius strip, you implement a screenwrap like the image below. But you also need to make it so that anything that goes through the interface will become its own mirror image. If the player goes through, you may even need to reverse the controls. Alternatively: have it work just like the normal wrap, but when the player goes through the ENTIRE SCENE gets mirror-image-flipped.
    mobius<br />image hosting gif<br /><br />

    Klein Bottle: what so it’s just a mobius strip with its sides glued together? WHAT WHY THE FUCK WOULD IT NEED TO LIVE IN A FOUR-DIMENSIONAL UNIVERSE?!
    So yeah here’s an animation showing 2 mobius strips becoming a Klein bottle.
    tumblr mo9l92 No0k1suhdw4o1 250<br />windows screenshot<br /><br />

    Klein bottles are pretty cool. I’ve worked on a project that used them to help understand the growth of neurons in the visual cortex! Can say more if you’re interested. It’s only a very slight change from the mobius strip, in terms of this game:

    klein<br />image upload no size limit<br /><br />

    Klein bottles are actually 4-dimensional shapes – the pictures of them you see are just 3D pictures of them! Or rather, 2D pictures of 3D pictures of the 4D klein bottle >;D

    COMING UP LATER:
    -Two holed torus
    -The amazing PROJECTIVE PLANE
    -Torus with two holes coming from an OCTAGONAL screen?! WHAT THE FUUUUU-
    -Explanation of why mathematicians and scientists care so much about this shit
    -if you want, I can say something about my work with the Klein bottle

    #221

    Lo-Fi
    Keymaster

    Hi Biological Topologist! When you first tweeted this info to me, I’ll admit I was confused (I am, after all, by no means a mathematician). After reading this over, though, it’s starting to make some sense. Let me see if I can relate some of this to what we’re working on.

    The sphere/map of the world: If I understand correctly, this would be headed in the sphere direction, correct?

    https://dl.dropboxusercontent.com/u/580413/SPSplitScreenWrap02.gif

    The major change needed would be to apply this to side-to-side wrap as well.

    Mobius strip: that video is super-cool! So, I just started messing with gravity flipping, as you can see in the latest kickstarter update (https://www.kickstarter.com/projects/lofi/four-sided-fantasy-a-game-about-the-limits-of-the/posts/985680).
    Would gravity flipping lend itself to being on a mobius strip? (One side = normal gravity, other side = flipped gravity). You say that to accomplish this, it would need to mirror-image anything upon screen wrap. Is that vertical or horizontal mirror-image?

    Klein bottle: your animated image isn’t animating, so I’m not quite sure I understand this one. Looked it up on Wikipedia, and it seems quite complicated! I like the elegance of the torus and mobius strip, not so sure about the Klein bottle. Can you go into more detail on this one?

    Thanks for the interesting angle on this! It would be really neat if I could find a way to relate each “ability” to some kind of shape or visual representation.

    Edit: My links are white, so you probably can’t see them! I’ll change that :P

    • This reply was modified 2 years, 6 months ago by  Lo-Fi.
    • This reply was modified 2 years, 6 months ago by  Lo-Fi.
    #273

    Re: mobius strip
    I think that it COULD lend itself to gravity-flipping, yes! So that we’re on the same page: let’s talk about the LEFT side of the screen connected to the RIGHT side of the screen in the mobius-strip way, so it’s just like gluing them together with a twist. You walk into the right side, and let’s say you’re close to the bottom of the screen. You come out from the left side, but now you’re closer to the top of the screen – your position has been mirror-flipped along an axis that goes straight across the middle of the screen. Also, the character (or whatever else goes through the interface) will be vertically mirror-flipped…

    This could work really elegantly with gravity flipping. In that gif on the kickstarter page, note that if you glue together the top and the bottom to get a tube, it still won’t look right, because the character will be turned upside-down, in a rather random looking way. I know you know this is a thing, because somebody had to write the code that vertically flipped the character’s sprite ;D So, I think you should do gravity flipping by joining together the *left and right* in a mobius-strip way.

    Note that in mobius strip mode, we have either the left connected to the right or the top connected to the bottom. NOT BOTH. The mobius strip has edges, like a simple elastic band, which you bump into. If you connect the top and bottom by the way, it would just be the character being *horizontally* flipped, which would make little apparent difference – unless, like I say, you make it so that pressing right makes the character go left and vice versa!

    Re: Klein bottle
    Here’s a better animation: https://www.youtube.com/watch?v=E8rifKlq5hc watch it a few times maybe.

    Implementing the klein bottle for you means: do the mobius strip “twist” connection for the left and the right, but then connect together the top and bottom as well in the ordinary way :) Couldn’t be simpler. Ignore all the obscure algebra stuff on the wikipedia page, it’s not at all important.

    Re: spherical
    Close, but not quite. For some reason I forgot to post this:
    ball<br />image posting<br /><br />
    make sense? You go through the left side of the screen, at the bottom say, and you come straight out of the left side again, but you’re at the top. That’s the same as what it would be on the world map I put up there, if you think about it. Actually there’s other ways of doing a “wrap” that correspond to a sphere. Here’s one:

    alt sphere<br />image hosting 10mb limit<br /><br />
    You’d get this sort of wrapping effect if you had a world map that looked like this:
    map<br />free image upload<br /><br />
    Though I can see why you wouldn’t like that, with the sides and top being different lengths. I can give you more options if you’re still interested in a spherical surface though?

    #276

    Hey I just watched the experimental features video again. As an elegant way of doing the “object change wrap”, how about you have that part be mobius strip, and the “object change” is a mirror-imaging. Obviously it’s up to you what objects this happens with, but for the sake of example let’s say there’s an L-shaped block and a tall ledge. Push the L shaped block over to the foot of the ledge and jump on top of the point of the sticking-up bit of the L. Try to jump up to the ledge, and though you do get high enough, you’re not far enough to the right.

    You use your mobius-strip-wrap and push the L into the interface, which is connecting the left and right of the screen. It turns into a Γ. Push that up to the foot of the ledge, and now when you get on it you can jump slightly further to the right and reach the tick.

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