SPOTLIGHT AI
× grandMA3

01パラダイムシフトParadigm Shift

02数式の力 — なぜ数式転送なのかPower of Equations — Why Transfer Math

数式が持つ本質的な優位性

The Fundamental Advantage of Equations

照明制御データには2つの表現がある。「毎フレームの座標値テーブル」と「座標値を生成する関数（数式）」。テーブルは有限だが、関数は無限を記述できる。これが数式転送の本質的な利点。

Lighting control data has two representations: "a table of per-frame coordinate values" and "a function (equation) that generates those coordinates." Tables are finite. Functions describe infinity. This is the essential advantage.

数式で表現できるパターンの豊かさ

Richness of Patterns Expressible Through Math

三角関数、ノイズ関数、剰余演算のわずかな組み合わせで、人間が直感的に「美しい」と感じる動きのほとんどを記述できる。以下は、ごく短い数式がどれほど多彩なパターンを生むかの例。

With just a handful of trigonometric functions, noise, and modular arithmetic, nearly every movement humans intuitively find beautiful can be described. These examples show how short equations produce remarkably diverse patterns.

数学的構成要素と表現力

Mathematical Building Blocks

これらの要素は自由に入れ子にできる。sin(noise(t))は「揺らぎのある周期」を、noise(sin(t))は「周期的に変調されるランダム」を生む。8つの構成要素の組み合わせは事実上無限のバリエーションを持つ。そしてそのすべてが数百バイトのJSONに収まる。

These elements nest freely. sin(noise(t)) produces "oscillation with organic variation." noise(sin(t)) creates "periodically modulated randomness." Eight building blocks yield effectively infinite variations — all fitting in a few hundred bytes of JSON.

JSONフォーマットの具体的メリット

Concrete Advantages of JSON Format

データサイズ比較

Data Size Comparison

03System Architecture

04AST JSON Specification

変換原理

Conversion Principle

// JavaScript
sin(t * 2.0 + i * 0.196) * 3.0

// AST JSON
["*", ["sin", ["+", ["*", "t", 2.0], ["*", "i", 0.196]]], 3.0]

プリセットJSON完全形

Complete Preset JSON

{
  "version": 1,  "name": "Spiral Galaxy",  "fixtures": 32,
  "equations": {
    "x":     ["*", ["sin", ["+", ["*","t",2.0], ["*","i",0.196]]], 3.0],
    "y":     ["*", ["cos", ["+", ["*","t",1.5], ["*","i",0.392]]], 2.0],
    "z":     ["+", ["*", ["sin",["*","t",0.8]], ["cos",["*","i",0.785]]], 1.5],
    "red":   ["+", ["*", ["sin",["+","t",["*","i",0.1]]], 0.5], 0.5],
    "green": ["+", ["*", ["cos",["+",["*","t",0.7],["*","i",0.2]]], 0.5], 0.5],
    "blue":  ["+", ["*", ["sin",["+",["*","t",1.3],["*","i",0.3]]], 0.5], 0.5]
  },
  "loop": { "start":0, "end":20, "repeat":-1 },
  "defaults": { "speed":1.0, "scale":1.0 }
}

ノード型・変数・関数

Node Types, Variables, Functions

変数: Variables: t (経過秒)(elapsed sec), i (正規化 0-1)(normalized 0-1), n (1-32), pi (π)

sin · cos · tan · asin · acos · atan2 · abs · sqrt · pow · min · max · floor · ceil · fmod · clamp · noise

05MA3 Lua Math Engine

ASTインタプリタ (loadstring不要)

AST Interpreter (no loadstring)

local ops = {
  ["+"]=function(a,b) return a+b end,
  ["-"]=function(a,b) return a-b end,
  ["*"]=function(a,b) return a*b end,
  ["/"]=function(a,b) return b~=0 and a/b or 0 end,
}
local fns = {
  sin=math.sin, cos=math.cos, abs=math.abs,
  sqrt=math.sqrt, pow=math.pow, noise=noise1d, ...
}
function eval(node)
  if type(node)=="number" then return node end
  if type(node)=="string" then return env[node] or 0 end
  local h = node[1]
  if ops[h] then return ops[h](eval(node[2]),eval(node[3])) end
  if fns[h] then
    local a=eval(node[2])
    if node[3] then return fns[h](a,eval(node[3])) end
    return fns[h](a)
  end
  return 0
end

06Lua Plugins

07Signal Flow & OSC

08動作モードOperating Modes

09Implementation Phases

10File Structure

grandMA3 Plugins

SPOTLIGHT AI 追加・変更SPOTLIGHT AI Changes

MA3 Executor

201: Speed    (0.1x~3.0x)    301: Preset ▲
202: Scale    (0.1x~5.0x)    302: Preset ▼
203: Aux      (0~1.0)        303: Engine Start/Stop
                              304: Shuffle

11Risks & Mitigation

12将来の拡張Future Extensions

13Resources