White-aster notation

White-aster notation is a notation for large numbers made by aster in a video on September 17, 2017https://www.nicovideo.jp/user/67584421https://www.nicovideo.jp/watch/sm31940678 from 11 min 40 sec.
This is an extension of Steinhaus-Moser Notation, which is one of the notations for large numbers. 
It is extended by adding the concept of stars and levels in addition to the usual polygons.
== Definition ==
First, we introduce the terminology to explain White-aster notation.
1.To simplify writing down the definitions, A string of integers greater than or equal to 3 or Ast is called a "figure type" as the only terminology used here, and a star is formally called "a Ast-gon".
2.For a figure of type p and integer n, a figure with <n> on the right shoulder of a regular p-gon is called "a p-gon of level n". For example, a regular triangle at level 4 is \(\triangle^{\langle 4 \rangle}\), and a star at level 5 is \(\textrm{☆}^{\langle 5 \rangle}\).
3.Let a be a figure or an integer greater than or equal to 3. A figure with an inside a p-gon of level n is denoted p[a,<n>] and called "a inside a regular p-gon of level n". For example, 3[5,<4>], which is 5 inside a regular 3-gon of level 4, is shown on the left in the figure below, 4[Ast[7,<6>],<5>], a 7 in a star of level 6 in a regular tetragon of level 5, is shown on the right below.
Based on this, the calculation of the White-aster notation is shown below.
Rule 1-1. If p = 3 and n=1, \[3[a,\langle 1 \rangle] = a^{a}\]
Rule 1-2. If p = Ast, \[\text{Ast}[a,\langle n \rangle] = a[a,\langle n \rangle]\]
Rule 2-1. If p = 3 and n > 1, \[3[a,\langle n \rangle] = \underbrace{\text{Ast}[\text{Ast}[\cdots[\text{Ast}}_{a}[a,\langle n-1 \rangle],\langle n-1 \rangle],\cdots],\langle n-1 \rangle],\langle n-1 \rangle]\]
Rule 2-2. If Rule 2-1 does not apply, \[p[a,\langle n \rangle] = \underbrace{p-1[p-1[\cdots[p-1}_{a}[a,\langle n \rangle],\langle n \rangle],\cdots],\langle n \rangle],\langle n \rangle]\]
== Examples ==
5[2,<1>]
=4[4[2,<1>],<1>]
=4[3[3[2,<1>],<1>],<1>]
=4[3[2^2,<1>],<1>]
=4[3[4,<1>],<1>]
=4[44,<1>]
=4[256,<1>]
This value is equal to Mega.
4[3,<2>]
=3[3[3[3,<2>],<2>],<2>]
=3[3[Ast[Ast[Ast[3,<1>],<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[3[3,<1>],<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[33,<1>],<1>],<2>],<2>]
=3[3[Ast[Ast[27,<1>],<1>],<2>],<2>]
=3[3[Ast[27[27,<1>],<1>],<2>],<2>]
…
== Issues ==
== Computation programs ==
* みずどら, 式神巨大数エントリー_編集中, Japanese Googology Wiki user blog. (Verified by Okkuu according to (2020-08-28)_式神巨大数の近況報告#11)
== See also ==
* White-aster
== Sources ==
Category:Notations
ja:白アスター表記