One-hour Mandelbrot: Creating a fractal on the vintage Xerox Alto

I wrote a short program to generate the Mandelbrot set on the Xerox Alto, a groundbreaking minicomputer from the 1970s. The program, in the obsolete BCPL language, ran very slowly—taking almost exactly an hour—but the result below shows off the Alto's monochrome bitmapped display. (Bitmapped displays were a rarity at the time because memory was so expensive.)

The Xerox Alto took an hour to generate the Mandelbrot set.

The Xerox Alto took an hour to generate the Mandelbrot set.

The Alto was a revolutionary computer designed at Xerox PARC in 1973 to investigate personal computing. It introduced the GUI, Ethernet and laser printers to the world, among other things. In the photo above, the Alto computer itself is in the lower cabinet. The Diablo disk drive (with the 1970s orange stripe) uses a removable 14 inch disk pack that stores 2.5 megabytes of data. (A bunch of disk packs are visible behind the Alto.) The Alto's display is bitmapped with 606x808 pixels in an unusual portrait orientation, and the optical mouse is next to the display.

Last year Y Combinator received an Alto from computer visionary Alan Kay and I'm helping restore the system, along with Marc Verdiell, Luca Severini and Carl Claunch. My full set of Alto posts is here and Marc's videos are here. I haven't posted an update for a while, but now I can write new programs and download them to the Alto using the Living Computer Museum's Alto file system implementation and gateway to the Alto's 3Mb Ethernet. I decided to start with the Mandelbrot set to take advantage of the Alto's high resolution display.

Marc's latest video shows the Mandelbrot programming running on the Alto.

The Mandelbrot program

The Mandelbrot set algorithm is fairly simple. Each point on the plane represents a complex number c. You repeatedly iterate the complex function f(z) = z^2 + c. If the value diverges to infinity, the point is outside the set. Otherwise, the point is inside the set and the pixel is set to black. Setting the pixel is tricky because the Alto doesn't have a graphics API; you need to determine which bit in memory to set.4

Since the Xerox Alto doesn't support floating point1, I needed a way to represent the numbers with its 16-bit word. I use fixed point arithmetic: 4 bits to the left of the decimal point and 12 bits to the right.2 For instance, the number 1.25 is represented in 16 bits as 1.25*2^12 = 0x1400. These fixed point numbers can be added with standard integer addition. After multiplying two fixed point numbers with integer multiplication, the 32-bit result must be divided by 2^12 (i.e. shifted right by 12) to restore the decimal point location.3

The code (above) is written in BCPL, the main language used on the Alto. BCPL is a precursor to C and many features of C are clearly visible in BCPL: everything from lvalues and rvalues to the ternary operator. You can think of BCPL as C without types; the only BCPL types are 16-bit words along with C-like structs, unions and bitfields. BCPL may look unfamiliar at first, but the code above should be clear if you consider the following syntax differences with C:

  • Blocks are indicated with [ and ] instead of { and }.
  • Indexing is with a!1 instead of a[1].
  • And, Or, and Shift bit operations are &, %, and lshift/rshift.
  • Variable definitions use let.
  • Arrays are defined with vec.

More information on BCPL is in the BCPL Reference Manual and my earlier article on using BCPL with the Alto.

The Xerox Alto, a few minutes into generation of the Mandelbrot set.

The Xerox Alto, a few minutes into generation of the Mandelbrot set.

Why is the Alto so slow?

Running the Mandelbrot set illustrates the amazing improvement in computer speed since the Alto was created in 1973 and the huge changes in computer architecture. On a modern computer, a Javascript program can generate the Mandelbrot set in a fraction of a second, while the Alto took an hour. The first factor is the Alto's slow clock speed of 5.88 MHz, hundreds of times slower than a modern processor. In addition, the Alto doesn't execute machine instructions directly, but uses a relatively inefficient microcode emulator that takes many cycles to perform one machine instruction.

The ALU board from the Xerox Alto. The Alto doesn't use a microprocessor chip, but a CPU built from three boards of integrated circuits.

The ALU board from the Xerox Alto. The Alto doesn't use a microprocessor chip, but a CPU built from three boards of integrated circuits.

Unlike modern computers, the Alto doesn't use a microprocessor chip, but instead has a CPU built from three boards full of simple TTL chips. The photo above shows the arithmetic-logic unit (ALU) board, which uses four 4-bit 74181 ALU chips to perform addition, subtraction and logic operations. You can also see the CPU's registers on this board. The Alto doesn't include a hardware multiplier, but must perform multiplication by repeated shifts and adds. Thus, the Alto performs especially poorly on the Mandelbrot set, which is essentially repeated multiplications.

Conclusion

The Mandelbrot set was a quick program to try out the Alto's graphics. Next I'll try some more complex projects on the Alto. If you want to run my code, it's on Github; you can run it on the ContrAlto simulator if you don't have an Alto available.

If you're interested in retrocomputing fractals, I also generated a Mandelbrot on a 50 year old IBM 1401 mainframe The 1401 generated the Mandelbrot set in 12 minutes—not because it's a faster machine than the Alto, but because the resolution on the line printer was very very low.

Mandelbrot generated on the IBM 1401 mainframe.

Mandelbrot generated on the IBM 1401 mainframe.

Notes and references

  1. There is a floating point library (source) for the Alto. I decided not use use it since the integer Mandelbrot was already very slow. But using floating point would make sense if you wanted to zoom in on the Mandelbrot. 

  2. Fixed-point arithmetic is a common trick for fast Mandelbrot calculation. 

  3. To multiply two 16-bit numbers efficiently, I use the double precision MulFull function (written in Nova assembler) in PressML.asm, part of the Computer History Museum's archived Alto software. 

  4. The hardest part of generating the Alto Mandelbrot was figuring out how to configure the display memory and update it correctly. The details on how the display works are in chapter 4 of the Xerox Alto Hardware Manual. To summarize, the display contents are defined by a linked list of display control blocks (DCBs), which define a rectangular region of pixels on the display. A microcode task reads 16 words of pixels from memory at a time and writes them to the display board, which shifts the pixels out to the monitor. Thus, as each scanline is being written to the CRT, the CPU is busily reading the pixels for that line from memory and feeding them to the display, another reason why the Alto is slow.

    The Alto's Smalltalk environment has a simple graphics API, but we don't have Smalltalk running yet.