Snap! Array Notation: Planar Arrays

Computer Science Math
1

Since BEAF Planar arrays are too complex for me to put in Snap!, I decided this is it's own notation and it will have it's different way of expressing multidimensional arrays. Expected Growth Rate in FGH: fw^(w2)(n). Growth Rate in BEAF in FGH: fw^w^2(n)
Project:
Snap! Array Notation Planar Array Calculator
V1 (Based off Linear Array Notation 3.0):
Snap Array Notation_ Planar Arrays script pic

Snap Array Notation_ Planar Arrays script pic (1)
Snap Array Notation_ Planar Arrays script pic (1)1160×4608 1.22 MB

Now that is a long script.
"n..." = first row
"o..." = second row
Hyperal = {10,10(1)10,10} in BEAF which is {10,10}(10,10) in the Snap! Array notation.

2

i cant even read the block definition its too long
what exactly does this do

3

I made a previous post about Linear array notation, where the rules are as follows (# means rest of array):
{a} or {a,1,#} or {a,1,1,1...} = a
{a,b} or {a,b,1,1,1...} = a^b
{a,b,c,d,#} = {a,{a,b-1,c,d,#},c-1,d,#}
{a,b,1,1...1,1,c,d,#} = {a,a,a...a,a,a,{a,b-1,1,1...1,1,c,d,#},c-1,d}
other:
{a,b,2} = a^^b or a^a^a^... b times
{a,b,3} = a^^^b or a^^a^^a^^... b times
{a,b,c} = {a,{a,...,c-1},c-1} b times
Basically this is the extended version (which is what is shown in the big script):
{a,b}(1) = {a,a,a,a,...} b times
{a,b,c}(1) = {a,{a,...,c-1}(1),c-1}(1) b times.
{a,b}(2) = {a,a,a,a,...}(1) b times
{a,b}(1,2) = {a,b}({a,b}(1))
{a,b}(c,2) = {a,b}({a.b}(...)) c times
{a,b}(c,3) = {a,b}({a,b}(...,2),2) c times
{a,b}(c,d,1,1...1,1,e,f,#) is same thing as {a,b,1,1...1,1,c,d,#} but it's on the (...)
The final growth rate is f_(w^(w2))(n) in FGH.

4

i still am clueless. this seems a little too complicated for me!

5

same here
i had a stroke reading the linear array notation post

6

can you provide examples of its use so its easier to understand

7

Search it up on googology wiki "Introduction to BEAF"

8

It's a notation to represent extremely large numbers, mostly too large for computers to do arithmetic on. So I don't think it has any "examples of use."

9

So large that even after it finally computes, it will still say "Infinity" or throw "bad digit radix 10"

10

so like a number thats very big but doing scientific notation isnt helpful because most of the didgets dont have identical neighbors?

11

Linear array notation can denote numbers way bigger than even graham's number (its {3,65,1,2}),
This notation can denote numbers not denotable in linear arrays.

12

Think about a number like 101,000,000. It won't fit in floating point, which has a limit of, I forget, 10three hundred something.

And that's before you even try to record its digits. If you want an exact representation of a number in that range, you need room in your computer for a million digits. Well, I guess that's just about possible these days, so let's think about a trillion digits, or a quadrillion digits. We're talking about very large numbers!

But it's possible to represent a few such numbers exactly, by using a representation other than a string of decimal digits. As an example of what I mean, you can't represent all the digits of pi in a computer, because there are of course infinitely many digits and they don't have any kind of repeating pattern. But it is possible to represent pi exactly in a computer: 𝜋. That's a Unicode character, so it can be inside a computer, and in fact I can make it magically appear on your computer screen -- look a line or two up! So if you and I agree ahead of time that that character represents the exact ratio of the circumference of a circle to its diameter, we're all set. So when @polymations says things like "{3,65,1,2}" they're doing something similar, using a previously-agreed-on notation to represent a small (compared to all the integers) set of numbers exactly.

13

to be specific, around 10309 or 21024

14

Thank you. I did pretty well for from-memory that I learned about 50 years ago.