blake447 - Tumblr blog

[blake447]

nD chess is now on android!

The apk is hosted on itch.io. future versions will be cross play compatible, and feature partial controller support. Now you can horrify your friends on the go!

[blake447]

I want people to stop telling me "nD chess when?" because I get that alot lol. So, guess what. nD chess now. Well soon at least. We got the vector math functioning, the out of bounds calculation and the orientation of the board actually need a little bit of work but once that's done we'll have nD chess, like in xkcd. This is the one I'm refering to.

I blame you guys for this unreadable, unbalanced mess lol.

[blake447]

Unfortunately, while our first 4D time travel game would have ended in my defeat, it ended up with something worse... Me discovering a a bug with the save / load feature. It seams loading from a file doesn't know how to properly handle double pawn motion, and likely queen promotion, leading to some corruption of the timelines. I've narrowed down where and why the bug is happening, but now... how to fix it

[blake447]

So adding on to the work i've been doing with integer sequences that generate fravtal curves, we have the hilbert curve, which ends up a bit more... Complicated than some of the others

So we start with our usual set up. Each number represents an absolute heading we wish to travel, and we start with a generating shape. What we are going to do is try to fold segments of the loop inward to create the shape everyone associates with the hilbert curve

In this case we start with 103. Now we start with a sequence detection. Basically we're looking for triples of ascending or descending order mod 4. When we find them, we expand them by a factor of five, since thats how many segments the hilbert curve will have on that edge.

After that we decide which segments to replace. In this case its always the same, first non consecutive pair, last non consecutive pair, and the one dead in the middle of the middle segment.

What we replace them with is whatever pushes the segment between the two paired numbers into the inside of the loop, and we can do that by referencing the other directions in that loop like so. The first and last non consecutive pairs reference the middle direction and its opposite, and the middle non consecutive pair references the start and end direction. Note we can rotate something 180 degrees by adding 2 to it (mod 4)

Here is the process in code

And here is the result! I've never quite liked the regularity of the hilbert curve, but I wanted to tackle it because I've already done a fair amount of work with other curves, so i didn't want to exclude this one!

[blake447]

Please enjoy this failed attempt at making a hilbert curve, which I would like to call a hilbert planter! Basically we got some sign error stuff going on. A bit more study is needed to find some greater pattern to the original fractal, but until then I kind of like this one's appearance

Here's the snippet of code to iterate this sequence. Won't elaborate much further, check out my posts on dragon curves and sierpinski curves for more info, its similar to those.

And one more at the next iteration

[blake447]

That was a lot of chessposting. Have some quaternion julia sets, as a treat These act as 3D slices of 4D extensions of julia sets. I believe this one is cubic in nature. To render these we use some math I dont understand from this blog to generate a distance estimator that can then be used to raymarch the sets. Raymarching is essentially marching along rays coming from the camera, only moving as far as we know we can move safely in any direction, until we hit something. This safe distance is where the distance estimator comes in. Anyways pretty pictures

This one I have a 3D print of

And this one I've colored the slice of it based on the coloration of the corresponding 2D julia set

[blake447]

The game has officially ended with whites resignation, I have lost after several queens have promoted on the enemy side and cleared the way for even more queens Some key takeaways, early queen trades made the board relatively safe as far as smothered checkmates go. The king just has too much motion to corner with non-queen pieces. Incidentally, this also makes utilizing the king a an offensive piece a fairly viable strategy, and without proper defensive positioning, the king can slip behind the back lines and wreak havoc, though I did risk being checkmated more than once that way.

Speaking of proper defensive positioning, my opponent Sapphia absolutely killed it with hers. This bubble was nigh impenetrable by any means, and served as a monument I could not tear down

On top of that, she activated her power pieces earlier and far more effectively, especially her dragons and unicorns, out maneuvering me at almost every turn with them. Her 4D intuition is significantly stronger than mine, which is perhaps not unsurprising because she has her own chess engine for 4D chess. Behold, the dreaded dragon chetto

The top hyperplane was nearly entirely wiped out during a long a vicious struggle for queen promotions. Being down key power pieces, I was unable to hold her off for long. My only saving grace was good offensive king strategies, until she moved her king in to defend, effectively shutting me down permanently Following that was a systematic and brutal elimination of all obstacles to further queening, eventually turning the game into a war of extermination, from which I had no chance but to surrender, or slowly and quietly go down in a prolonged struggle

All in all, fun game. Has some slow points, but picked back up during the queening race. Absolutely intimidating, and defense pays off a little better than offense, or at least ill-thought out offense like all of my strategies were. Next time we have a new game variant to try out.

Or we'll relax with some nice, simple, multiverse time travel chess

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

We broke the line but all forces were devestated or pinned down. The king is now on the run, queening of the enemy forces is eminent. I fear the next update will be one of my defeat, nay, I know so. it was nice while it lasted!

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

Day 2 of the 4 Dimensional Siege. The bubble stands strong. The troops are weary, those that are still left anyway. The high commanding king has abandoned them to take matters into their own hands. I fear the battle may come to a close soon, but not in a way that is favorable

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

Ooh, also I've done a similar program with rounded edges by fudging some magic numbers!

And some more pretty pictures just for the heck of it, collected from linked posts

So in case anyone's following and seen my work with dragon and koch curves, and was curious about sierpinski's triangle, it can be represented with these sequences but unfortunately the process is more irregular so we cant pull the same tricks with binary sequences, at least in any manner that is immediately obvious.

Pictured above is a process where you double each element of the sequence, and pick a number to inject smaller triangles into, then repeat the process. With a bit of practice you can draw an eularian path that forms a sierpinski triangle.

If you wanna get really fancy you can vary the edge you break into smaller triangles each iteration, though its really, really hard to do on the fly

This is one i've always wanted to write a program to generate.

[blake447]

Oh I've already done similar work with the dragon and koch curves, which have even more interesting variations. The sequence for the koch curve goes something like this start with 0 0 double it 00 between every pair inject +1 -1 (mod 6) 0150 double it 00115500 between every pair inject +1 -1 (mod 6) 0150 1201 5045 0150 assigning in increments of 60 degrees rather than 120. Even more interesting, is you can find a series based on binary bits that converges in something like n terms for the nth iteration that cuts the recursion out entirely, effectively parallelizing it. Here's my post for that The dragon curve is a classic. It goes like so start with 0 0 copy, reverse, add 1 (mod 4) and append 0 1 01 10 -> 0121 0121 1210 -> 0121 2321 Which again has a binary bitwise representation with similar convergence detailed here

This one is actually catalogued in the list of integer sequences funnily enough, though I think the way I've generated the two of them is novel, and if not independently discovered by yours truly.

So in case anyone's following and seen my work with dragon and koch curves, and was curious about sierpinski's triangle, it can be represented with these sequences but unfortunately the process is more irregular so we cant pull the same tricks with binary sequences, at least in any manner that is immediately obvious.

Pictured above is a process where you double each element of the sequence, and pick a number to inject smaller triangles into, then repeat the process. With a bit of practice you can draw an eularian path that forms a sierpinski triangle.

If you wanna get really fancy you can vary the edge you break into smaller triangles each iteration, though its really, really hard to do on the fly

This is one i've always wanted to write a program to generate.

[blake447]

I'm doing it, I'm attacking the bubble!

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

Update they saw through my line of attack like 14 turns ahead of me finishing setting it up. Everything takes so long to setup lol. Think I'm losing (white) they have much better pawn development

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

Okay this game mode is actually pretty hard lol. Currently playing somebody in 4D chess wish me luck!

[blake447]

Polygons are something insane. Pieces average at about 400 each (really? God it thought thay was better) and there are roughly 400 pieces on each board, so we're looking at 160,000 per board at least, though those are gpu instanced forbwhat its worth. Compared to that the boards themselves are negligable, at about 20*64 for 1280, so we'll ignore that in our estimate. Since we're estimating anyway and our estimates have been high, lets just drop it down to 150k per board for easy estimation, so at 18 boards we get something like 9*300k will be, on the order of magnitude of 2700k, or ~3mil

This is made in unity

And it is available on itch.io as nDimensional Time Travel Chess! Featuring less insane gamemodes as well

"They called me a madman"

Send help, my computer is *struggling* with this one. I don't even know why I'm leaving this as an option, probably because its just funny as hell to me lol. Human comprehension be damned, this is full blown 7 Dimensional Chess. We've got 5 spatial dimensions, count 'em 5. We're playing with a base board of 4x4x4x4x4 for 1024 squares and like 200ish pieces I dont feel like counting

Then we got 2 more dimensions, on in time, one multiversal.

This is perhaps, the single worst variant of chess in existence, if not the most incomprehensible. Now to find someone insane enough to play it with me

[blake447]

"They called me a madman"

Send help, my computer is *struggling* with this one. I don't even know why I'm leaving this as an option, probably because its just funny as hell to me lol. Human comprehension be damned, this is full blown 7 Dimensional Chess. We've got 5 spatial dimensions, count 'em 5. We're playing with a base board of 4x4x4x4x4 for 1024 squares and like 200ish pieces I dont feel like counting

Then we got 2 more dimensions, on in time, one multiversal.

This is perhaps, the single worst variant of chess in existence, if not the most incomprehensible. Now to find someone insane enough to play it with me

[blake447]

Been doing a lot of work on my chess engine lately. The first of which is I've added a neat little preview window (finally) that allows you preview the type of board that you'll be playing on. The multiverse preview will be completed at a later date

The next thing I've done is fixed a bug with the undo function in time travel variants of the game. Basically what happened is complicated combinations of multiversal and time travel moves would cause the undo function to be confused, and only half undo them. To solve this I added a stack that records the order at which boards were spawned in. Along with that I've added these snazzy purple arrows that show the relationship between timelines

Another thing I've done is fully implement en passant, in both regular and time travel variants. It does this by placing a ghost pawn as an additional command within a double pawn move, functioning very similar to a queen promotion.

Finally I've added a 6 wide variant of 4D chess (also time travel compatible of course) which should play more like traditional chess, just on 4 dimensional steroids. Haven't play tested it yet but hopefully its a lot of fun.

Friendly reminder you can check it out now on itch.io, and it has multiplayer functionality! Share your horror with your friends as you fumble around in up to 6 dimensional spaces