Buddy's Probably Terrible Array Notation (BPTAN)

average array notation

inspired by BAN (bird's array notation)

# ]
x
y

{\displaystyle [x,y] = x\uparrow y}

[
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[
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{\displaystyle [x,y,1] = [x,y]}

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[
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{\displaystyle [x,y,1,z,\cdots,a] = [x,y]}

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⏟

z

{\displaystyle [x,y,z] = \underbrace{[x,[x,[x,\cdots[x,y]]]]\cdots]}\_{z}}

An array of size 3 is equal to

a^a^...(c a's)^b

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⏟

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{\displaystyle [x,y,z,w,\alpha] = [x,y,\underbrace{[z-1,z-1,z-1,\cdots ,z-1]}\_{w},\alpha]}

so for example

[2,3,4,5] = [2,3,[3,3,3,3,3]] = [2,3,[3,3,3,[2,2,2]] = [2,3,[3,3,3,16]] = [2,3,[3,3,[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]]] = [2,3,[3,3,[2,2,[1,1],2...] = [2,3,[3,3,[2,2,1,2,2..] =[2,3,[3,3,4]] and etc.

Alpha is the rest of the list, btw

More? More.

yep theres more

### Hyper-Arrays

{
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,
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}

{\displaystyle \lbrace[x,y],[a,b]\rbrace}

=

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{\displaystyle [[x-1,x-1],[y-1,y-1],[a-1,a-1],[b-1,b-1]]}

If the number of numbers in the right bracket is bigger, (ex. {[x,y],[a,b,c]}), that would equal {[x,y],[a,[b,c]]}

If the number of numbers in the left bracket is bigger, same thing will happen

another example

{[x,y],[a,b,c,d]} would be {[x,y],[a,[b,c,d]]}

it turns the last few inputs into a normal array, where the amount of inputs are equal

MORE???

still yes

### DIMENSIONAL ARRAYS???

[
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1

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[
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{\displaystyle [a|1|b] = [a,b,2]}

[
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[

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⏟

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⏟

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{
[
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b
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,
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}

 is same as if the dimensional arrays were already normal arrays

### Expanded Dimensional Arrays

If we define the previous [a|x|b] function as

[
a

0

x

c
]

{\displaystyle [a|\_0x|c]}

, then we can add MOAR!!

[
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⏟

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The increase of the number adds another layer of recursion

### -tional Arrays

inspired by BEAF's tetrational arrays

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[
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[
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=
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↑↑
2

{\displaystyle [x,y](2) = [x,y]^{[x,y]} =[x,y]\uparrow\uparrow 2}

[
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(
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[
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↑↑
a

{\displaystyle [x,y](a) = [x,y]\uparrow\uparrow a}

[
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[
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{\displaystyle [x,y](1,a) = [x,y](a)}

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[
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)

{\displaystyle [x,y](2,a) = [x,y](1,[a,a])}

[
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[
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⏟

b

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{\displaystyle [x,y](b,a) = [x,y](b-1,\underbrace{[a,a,a,\cdots,a]}\_{b})}

you get the idea

### Step-Down Arrays

A "Step-Down" array has the dot AFTER the x, so for example [x\*,y,z] would have x become a Step-Down array.

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{\displaystyle [x\cdot \alpha] = [[x,x-1,x-2,\cdots,2],\alpha]}

 where alpha is the rest of the list.

### Slashes + -tional Arrays

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∖

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{\displaystyle [x,y](2\backslash\_{2}) = [x,y]([2,2](2))}

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{\displaystyle [x,y](a\backslash\_{b}) = [x,y]([a,a](b))}

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(

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⏟

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{\displaystyle [x,y](a\backslash\_{b,c}) = [x,y](\underbrace{[a,a,\cdots,a]}\_{c}(b))}

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⏟

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{\displaystyle [x,y](a\backslash\_{b,c,d\_{0},d\_{1},\cdots,d\_{n}}) = [x,y](\underbrace{[a,a,\cdots,a]}\_{c}(b\backslash\_{d\_0+1,d\_1+1,\cdots,d\_n+1}))}