lmjb1964 (hmm, this name seems familiar...) wrote:Just blows my mind. I used to be good at <mathy stuff>, and I suppose if I really sat down and worked through it, it would make sense. But it's been too long since I've done that kind of stuff, so I just get cross-eyed. I'll just continue to marvel at how your minds work, and admire the pretty colors.

If you want to find out more about wow the minds work then maybe this will be helpful:

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Part 4/2 - how I arrived at epilogueworld and what i did there

Until recently my knowledge about the

epilogue sequence was very limited.

I knew that there are 5 frames and that they are appearing every hour not randomly but in some pattern.

ggh, hujackus, slinches, maybe others too noticed some patterns and even made some predictions.

When reading their posts I wouldn't understand much what they were talking about.

But I didn't really try.

When I was making BFTF I started thinking about our epilogueframes a little.

Quickly decided that BFTF will not have such a thing.

But I also started thinking how I would generate such sequences.

I thought

I would probably not make such a nice thing as GLR did.

Instead I would just build it from some XORs, they make nice patterns. And also they mix the influence of different variables making them less obvious.

I had no idea how close to the truth I was then!

I didn't post anything about this so there is no way for me to prove it.

Then I stopped thinking about it again.

And then, it was 2018.

New year always brings the topic of

epilogue sequences back to the OTT.

And 2018 is special because it allows for new predictions for 2018-2021.

So OTTers start talking about it again.

Ucim asks what are the "sloshers".

My knowledge was that some patterns were identified but there are frames which don't fit those patterns and they are called "sloshers".

I decided to check if I'm remembering this correctly.

I found the page on mschaviewer describing the situation really well.

I learn about what the current understanding is.

But I'm actually trying to understand it this time.

So I learn that:

- there are only 5 different 4x4 squares
- the sequence seems to be based on decimal numbers interpreted as hexadecimal
- the year can be reduced to just 3 letters

Also from hujackus' picture I learn about the year patterns and the 90 degree rotation.

Wow that's so cool!

I decide to make a spreadsheet to illustrate this.

I wanted to see this in action to understand this better.

While making this spreadsheed I noticed more:

There aren't 5 different possible 4x4 squares. Actually there is only one! the 5 comes from shifting the "base" 4x4 square by different offsets (mod 5).Big enlightment.

Also, the expansion from the 3 letters to the letters representing each 4x4 square is also done just by applying offsets (mod 5).

So, in my spreadsheet,

I could expand from the 3 letters to the full year by just adding offsets and mod 5, nothing else was needed!I post the file and I keep thinking and reading

The 3 letters defining a year also seem to be arranged in 4x4 squares.

To predict the future we would have to know what is going to be the next square.

I look at it and I notice some regularity.

I make my first prediction.

Next day I'm not so sure about my prediction.

I think that it's much more likely to get a pattern break at 2020.

because if everything else depended on single digits then it's no reason why the year would be different.I'm still wondering why the patterns are how they are.

There is mod 5 everywhere but at the same time everything seems to be related with 4s.

I make a very lucky guess.

I guess that because I could expand the year using just addition then

it is very likely that the sequence generating function is built by adding multiple components depending on different variables.

Maybe at least some

components can be identified by analysing points where other variables are 0?

I look at the "outermost"

sequence.

Left column in

this picture.

everything else than year is 0.

ABDE EACD DEBC CDAB (BCEA?)

How could such a

sequence be built?

I see 4s and 5s in this.

after every 4 characters we get the same

sequence shifted by 5.

Let's start with adding (mod 5) mod 5 to mod 4.

Code: Select all

` 0123 4012 3401 2340 1234`

+ 0123 0123 0123 0123 0123

---------------------------

0241 4130 3024 2413 1302

Nice but useless.

But let's do something.

I'll start with assigning numbers to letters.

A = 0 because on the top left edge where everything is 0 there is A.

If we also consider how the squares are all the same but shifted we're left with only 2 possibilities:

01234 = ABCDE or 01234 = AEDCB.

The first one is more promising because then we have the same

sequence increased by 4, every 4 letters.

So the

sequence is now 0134 4023 3412 2301 (1240?)

Let's subtract mod 5 from it:

Code: Select all

` 0134 4023 3412 2301`

- 0123 4012 3401 2345

----------------------

0011 0011 0011 0011

Interesting...

Something different now.

the

sequence is repeating so maybe focus just on one repeat, 0134.

or rather the whole square:

How to build such a block?

I notice the 2x2 chessboard patterns of two kinds of 2x2 squares which also have this chessboard.

Where have I seen this before?

Suddenly, I know.

XOR!

xors everywhere!

xors produce such patternsIf i xor the lowest bits of the year and the tendays i get this:

And if I do the same with the next bit I get this:

But actually, what I get is this:

when the operation is performed on whole numbers and not on isolated bits.

Ok, what next?

how to build the square from these parts?

Simply adding them will not work:

Two of the 2x2 squares are correct, two other are off by 1.

What I really need is this:

But how do I transform nicely

into

?

No, wait I don't have to .

I realise something.

I have to add a 3 but all I have is some 2s.

But

in mod 5 adding 3 is the same thing as subtracting 2.Let's try:

Yes!

That's what I needed.

Now I have a nice way to generate the most basic of squares.

At this point I feel like nothing can stop me now.

So now to continue with the rest of the yearcube

what do I need to add to the base square to produce the correct

sequence?

Let's see:

So I need something that removes 1 every 4 years or somethings that adds 4 every 4 years.

The second option seems more promising.

Add a 4 every 4?

Is there a nice way to do it? preferable a bit operation?

Yes, I just have to ignore the 2 lowest bits, or, in other words do an AND 0xC operation.

I get a 0 0 0 0 4 4 4 4 8 8 8 8 12 12 12 12

sequence which is the mod 5 equivalent of what I need:

Very good, I can generat the whole yearcube now!

This is already a success.

The next thing to do is to try to find a way to expand a year's 3 letters into the whole year.

Because the fullyear pattern is similar to the yearcube pattern it is very likely that also their generation will be similar.Again, I start with the most basic square:

It's similar but different.

I know. I see it.

It goes backwards.

Even more:

the full year base square is the negative of the year cube base square. They add up to 0:

If so, I can just replace this

with this

And success. the base square generator is ready. That was fast.

Now there's just one thing left to do.

What to add to the squares to produce the full pattern?

Let's see:

I decide to expand it this way:

There are multiple reasons for this:

- the patterns are consistent
- it aggrees with hujackus' extension
- it is the same as the top of the year cube's base square: 0134
- it seems to be the most promising

But even if this is not correct it doesn't matter at all.

because it can only effect digits higher than 9 which is not something we can see in the real world.

So how do I build this?

By similarity to this

I could expect something like this:

But that's wrong, unfortunately.

I cannot generate 0101 or 0022 with simple bit operations because those patterns are actually 0000111100001111 and 0000000022222222.

These are on different bits.

If I did the AND operations on the correct bits I would get 0000444400004444 and 0000000088888888.

And this is actually good news, because of mod 5.

In mod 5 subtracting 4 is the same as adding 1. and adding 8 is the same as subtracting 2.So I try this

And this is correct.

And with this I have all the parts!

Great success!

I almost don't believe it but I have managed to find a successful

epilogue sequence generator.

Now the only thing left to do was to post it in an easily understandable way...

Redundant