Modulo马杜罗操作符讲解和余数的周期性

To understand why $sequence_val = ($count % 3) * 50; creates that specific pattern, you have to look at it in two steps: the Modulo (the “Reset” button) and the Multiplier (the “Scale”).

1. The Modulo ($count % 3)

% 马杜罗操作符返回两数相除的余数

The modulo operator % returns the remainder after division. When you divide any incrementing number by 3, the remainder can only ever be 0, 1, or 2.

Think of it like a clock with only three numbers. As you count up, the pointer just keeps spinning around those three spots:

Loop Count	Calculation	Remainder (Result)
0	$0 \div 3 = 0$ with remainder 0	0
1	$1 \div 3 = 0$ with remainder 1	1
2	$2 \div 3 = 0$ with remainder 2	2
3	$3 \div 3 = 1$ with remainder 0	0 (Reset!)
4	$4 \div 3 = 1$ with remainder 1	1

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2. The Multiplier (* 50)

Now that you have a sequence that only produces 0, 1, 2, you simply multiply that result by 50 to scale it to the values you want:

• 0 $\times 50$ = 0
• 1 $\times 50$ = 50
• 2 $\times 50$ = 100

When the loop hits the next number (3), the modulo resets to 0, and the whole math starts over: $0 \times 50 = 0$.

Summary Table

Here is how it looks inside your WordPress while loop as it runs:

Post Number	$count	$count % 3	Result (* 50)
Post 1	0	0	0
Post 2	1	1	50
Post 3	2	2	100
Post 4	3	0	0
Post 5	4	1	50
Post 6	5	2	100

If you ever wanted the sequence to be 0, 20, 40, 60, you would simply change the formula to ($count % 4) * 20.

Would you like to see how to use this to add different CSS classes (like delay-0, delay-50, delay-100) to your WordPress posts?

How the Modulo Operator Works

This video provides a clear mathematical breakdown of how the modulo operator calculates remainders, which is the core logic behind your repeating sequence.

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1. 余数的周期性（周期为除数）
更具体地说，这体现了 模运算（Modular Arithmetic） 的基本性质。

在模 $m$m 的系统中，整数集被分成 $m$m 个剩余类（residue classes）：$$[0{]}_m,[1{]}_m,\dots ,[m-1{]}_m$$[0]m​, [1]m​, …, [m−1]m​

其中 $[r{]}_m=\{n\in \mathbb{Z}\mid n<mrow\; style="border-color:\; currentcolor;"><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">m</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">o</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">d</mi></mrow>m=r\}$[r]m​={n∈Z∣nmodm=r}。

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2. 在数列中的体现
递增整数 $n=0,1,2,3,\dots$n=0,1,2,3,… 除以 $m$m 的余数，就是 按顺序循环遍历所有剩余类，这个序列有时称为 余数序列（residue sequence）。

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3. 相关的重要概念/名称

• 在离散数学或组合数学中，描述这种整数依次取模结果循环的现象，常称为 循环取模序列。
• 在初等数论中，它就是 模 mm 的完全剩余系（complete residue system modulo mm） 的循环出现。
• 若从余数函数 $f(n)=n<mrow\; style="border-color:\; currentcolor;"><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">m</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">o</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">d</mi></mrow>m$f(n)=nmodm 的角度看，这是一个周期为 $m$m 的周期函数（定义在整数上）。
• 在计算机科学中，这种递增取模的结果循环，有时会称为 modulo cycling。

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所以，要一个最标准的术语：

模 mm 的余数序列以周期 mm 循环，或者更精确地说，$n<mrow\; style="border-color:\; currentcolor;"><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">m</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">o</mi><mi\; mathvariant="normal"\; style="border-color:\; currentcolor;">d</mi></mrow>m$nmodm 是一个周期为 $m$m 的周期函数（定义域为整数）。

如果你想要一个简洁的“专属名词”——
“模 mm 周期循环（modulo-m cyclic sequence）”比较贴切。