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于 2026 年 5 月在 Ommen, Netherlands 举行的 Outline Demoparty 上发布的 "wake up! 16b" 是一件引人注目的 demoscene 作品：它在仅用 16 字节 x86 实模式 DOS 汇编代码的条件下，探索了算法密度的极限。运行时，程序把显存既当作计算空间又当作显示缓冲区，用以渲染无限的谢尔宾斯基三角形，同时将这些几何数据解释为发送到 PC 扬声器的音频。整段程序仅由八条指令组成，总共 16 字节，可谓极简编码的极致实践。

代码以 int 10h 开始，初始化视频模式 0（40×25 字符文本模式）。随后两条指令将数据段寄存器指向 0xB800（VGA/CGA 文本缓冲区的物理地址）。在该中断清屏时，BIOS 会用统一模式填满所有 2000 个字符槽：ASCII 0x20（空格）和颜色属性 0x07（黑底浅灰）。表面上看似空白，实际上是一块填充了可预测、均匀数据的画布。这种均匀性至关重要，因为数学递推依赖一致的初始状态；内存中的任意随机伪影都会破坏分形，就像意外的一位能损坏元胞自动机那样。

程序的核心通过一个循环实现累加前缀和式的变换。 lodsb 从内存加载一个字节到累加器 AL，随后 sub si, byte 57 将源索引向后调整 56 字节（补偿 lodsb 的隐式自增）。接着 xor [si], al 把累加器与该位置的内存做异或，并把结果写回内存，从而在内存中形成一种"运行前缀和"的累积效果。在用 add 代替 xor 、步长为 16 字节且起始值为 2 的简化模型里，数值会按二项式系数序列累积；文章用表格演示了 16 个内存单元在 16 次遍历中逐行累加的过程，说明了这一数学递推。

关键在于用异或替代加法。二进制加法会产生进位并影响相邻位平面，而异或丢弃算术进位，等价于模 2 加法。起始值为 2（二进制 00000010），因此只有第 1 位会被影响。这把位平面隔离开来，使得值在 0x00 与 0x02 之间纯粹切换，恰好对应 Stephen Wolfram 的初等元胞自动机中的 Rule 60 。文章用第二个表格验证了这一点：第 1 位的置位与清零模式形成了典型的谢尔宾斯基三角形结构。

音频生成是该设计中最优雅的部分之一。 out 61h, al 将计算出的字节直接送到端口 61h，该端口连接内部 PC 扬声器。端口的第 1 位直接控制扬声器振膜：为 1 时向外推动，为 0 时回位。因为算法专门隔离并翻转第 1 位，谢尔宾斯基三角形的几何结构就直接变成了驱动扬声器振膜的指令。 CPU 的执行速度决定了有效采样率，1 与 0 的序列产生不同脉宽和频率的方波。交替的行会生成更高频的方波，而三角形内部的大块 0 区域则制造出节奏性的停顿，从而把数学结构直接转化为可听的声音纹理。

向后步进 56 字节（通过 sub si, byte 57）而不是向前步进 16 字节，对视听输出影响显著。 16 字节步长会在 4096 次迭代内完成一段扫掠，而 56 并不能整除 65536，需要 8192 次迭代才能访问所有地址，并在回到零之前绕段循环 7 次。这使宏周期加倍、基频减半，听起来下降一个八度，产生更慢更沉的音色。程序把结果写入 ASCII 字符字节：第 1 位用于控制扬声器，其余 7 位则演化出伪随机的 ASCII 字形，作为视觉纹理。值得注意的是，把这些混合数据发送到端口 61h 并不会导致系统崩溃，因为在标准 DOS 环境和常见模拟器中，多余的位会被无害地忽略。

在 40 字符宽显示上，-56 字节步进会产生对角剪切效果。向后 56 字节等同于在 80 字节行宽上向前 24 字节，即恰好 12 列；每个字符占 2 字节，因此序列每步上升 1 行并向右移动 12 列。由于 gcd(12,40)=4，循环恰好访问四分之一的列（40 列中的 10 列），于是分形以 10 列等间距的竖列形式在屏幕上向上展开，而非呈现为连续图像。

文章最后指出了对内存初始状态的依赖。理论模型假设环境被完美初始化，但实际中不同的系统配置、 VGA BIOS 实现和模拟器会在 RAM 中留下各种伪影。由于算法不断地读取并与现有内存内容做异或，它会直接与这些位交互，因而输出对运行环境高度敏感：视觉字符与音色在不同机器或模拟器上可能明显不同。虽然加入初始化例程以显式清除内存可以保证输出一致，但那会超出严格的 16 字节限制。接受这种微妙的不确定性，恰是在人为极限条件下创作的魅力所在。 Released at the Outline Demoparty in May 2026 in Ommen, Netherlands, "wake up! 16b" is a remarkable demoscene production that explores algorithmic density within just 16 bytes of x86 real-mode DOS assembly code. When executed, it uses the computer's video memory as both a calculation space and a display buffer to render an infinite Sierpinski fractal, while simultaneously interpreting that geometry as audio data sent to the PC speaker. The entire program consists of only eight instructions, totaling 16 bytes, making it an extreme exercise in minimalist coding.

The code begins with `int 10h`, which initializes Video Mode 0, setting up a 40x25 text mode display. The next two instructions point the Data Segment register to `0xB800`, the physical memory address of the VGA/CGA text buffer. When the BIOS clears the screen during this interrupt, it fills all 2,000 character slots with a uniform pattern: ASCII byte `0x20` (Space) and color attribute `0x07` (Light Gray on Black). While the screen appears blank, it is actually a canvas primed with predictable, uniform data. This uniformity is critical because the mathematical progression relies on a consistent starting state. Any random artifacts in memory would disrupt the fractal pattern, much like an unexpected bit can corrupt a cellular automaton.

The core engine of the program operates through a loop that creates additive prefix sums. The `lodsb` instruction loads a byte from memory into the accumulator `AL`, then `sub si, byte 57` adjusts the source index backward by 56 bytes (accounting for the implicit increment from `lodsb`). The `xor [si], al` instruction then XORs the accumulator value with the memory at that location, storing the result back. This creates a running prefix sum effect where values accumulate across memory. In a simplified model using `add` instead of `xor` with a step of 16 bytes and starting value of 2, the values follow a binomial coefficient sequence. The article includes a detailed table showing how values accumulate row by row across 16 memory cells over 16 passes, demonstrating the mathematical progression.

The key insight comes from replacing addition with XOR. When performing binary addition, bit-planes carry over into adjacent positions, but XOR discards the arithmetic carry, effectively performing addition modulo 2. Since the starting value is 2 (binary `00000010`), only Bit 1 is ever affected by this calculation. This isolates the bit-planes and creates a pure toggle between `0x00` and `0x02`, mapping perfectly to Rule 60 in Stephen Wolfram's elementary cellular automata. The article validates this with a second table showing the binary propagation, where the pattern of Bit 1 being set or cleared forms the characteristic Sierpinski triangle structure.

The audio generation is perhaps the most elegant aspect of the design. The instruction `out 61h, al` sends the computed byte directly to port `61h`, which interfaces with the internal PC speaker. Bit 1 of this port directly controls the speaker cone, pushing it outward when set to 1 and returning it when set to 0. Because the algorithm specifically isolates and toggles Bit 1, the geometry of the Sierpinski triangle serves as direct instructions for the speaker cone. The CPU's execution speed establishes the functional sample rate. The patterns of 1s and 0s generate distinct square waves with varying pulse widths and frequencies. Alternating rows produce higher-frequency square waves, while larger blocks of zeros (the empty regions within triangles) create rhythmic pauses, resulting in a direct sonic representation of the mathematical structure.

The choice of stepping backward by 56 bytes (via `sub si, byte 57`) rather than forward by 16 has significant consequences for both audio and visual output. While a 16-byte step completes a segment sweep in 4,096 iterations, 56 does not divide 65,536 evenly, requiring 8,192 iterations to hit all addresses and wrapping around the segment 7 times before returning to zero. This doubles the macro-cycle length, halving the fundamental frequency and dropping the auditory rhythm by one octave, producing a slower, deeper tone. The algorithm writes to ASCII character bytes where Bit 1 controls the speaker, while the remaining seven bits mutate into pseudo-random ASCII glyphs for visual texture. Remarkably, sending this mixed data to port `61h` doesn't crash the system, as the extra bits are harmlessly ignored in standard DOS environments and emulators.

Visually, the -56 byte step creates a diagonal shearing effect on the 40-character wide display. Stepping backward by 56 bytes is equivalent to moving forward by 24 bytes on an 80-byte grid, which equals exactly 12 columns. Since each character space occupies 2 bytes, the sequence progresses up 1 row and right 12 columns per step. With gcd(12,40)=4, the loop visits exactly one-quarter of the columns (10 out of 40), rendering the fractal as 10 evenly spaced vertical columns ascending the screen rather than a contiguous image.

The article concludes with an important observation about memory dependency. The theoretical model assumes a perfectly initialized environment, but in practice, different system configurations, VGA BIOS implementations, and emulators can leave varying artifacts in RAM. Since the algorithm continuously reads and XORs against existing memory contents, it interacts directly with these bits, making the output highly sensitive to its environment. Visual characters and audio timbre may vary noticeably across different machines or emulators. While adding a setup routine to explicitly clear memory would ensure identical output, it would exceed the strict 16-byte limit. Embracing this subtle unpredictability is presented as part of the charm of working within such extreme constraints.