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Comment by LectronPusher | Hacker News Reader

This was fun, I forget sometimes how silly all our grade school math worksheets used to be. I always had trouble showing my work for simple additions and multiplication, it's a bit easier when its a self motivated dunking on the GPUs.

It may take 4-5 days and 1000+ people, but it's definitely created a greater sense of community than any faster rendering system. I like looking over the different pixels and knowing that they represent some nerd-sniped engineer like me.

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I think something like this would actually make for a really interesting 3rd grade class project, with each student contributing a few pixels.

Ah, I remember seeing some chinese summer math workbook shared online where the answers to each problem could be translated into a bit that could be plotted in a giant grid on the last page.

When completed, it would show a QR code, that upon scanning would mark completion of the workbook and show you the answer key. The implicit idea being you didn't have to be perfect, just good enough so the error-correction algorithm of QR codes was enough to pick up the final image. (Probably extra credit if you could figure out how to do as few problems as needed and then use EC to still figure out the secret link)

This is so genius - if I ever become a teacher I'm doing this.

That's pretty clever... QR codes even allow you to set the percentage of error correction allowed.

It's slightly older than 3rd grade, but for Pi Day 2022, Matt Parker marshaled a couple dozen students to spend a weekend computing pi by hand: https://www.youtube.com/watch?v=dtiLxLrzjOQ

It's really interesting seeing the (what I assume are) error pixels.

The author should implement an error correction system, where 1) the result is withheld from the display until a second corroborating calculation comes in, and 2) if there is disagreement, request an arbitration from a third user whose job is to pick which of the two is the best answer.

I don't know, if they were aiming for perfection you'd think they'd just use a computer.

It is a bit odd; they specifically ask for the picture of the worksheet, and say they’ll check it. I wonder if the just haven’t gotten around to it yet. Automatic error checking would be nice (IMO just let multiple people do each pixel and take the most popular result).

They ask for the worksheet to check that you're not cheating. They don't check the pixel values. I think much of the charm of the image is seeing the errors.

By the way, there's more going on in the shader algorithm than you might expect. Here's an explanation of the worksheet:

  u, v are coordinates relative to the center of the image
  h is radius from center, squared
  Section B generates the ball:
  B3-8 generates the reflected color on the ball.
  B9-11 applies the diffuse illumination to the ball.
  B12 adds the illumination highlight.
  Section C creates the ground:
  C5 puts a shadow directly under the ball.
  C13 is the cast shadow of the ball.
  Section D creates the sky with a simple gradient
  Section E converts the image from two-color to three-color

Hello, my name is Inigo Quilez, you skilled my father, prepare to draw half the shader on shadertoy :D

They already know the right answer for each pixel, presumably though?

If they didn't then maybe they could write some kind of computer program to find them.

The errors (wrong colors) colors is the charming part to me.

Or a story if anti-aliasing but getting each pixel computed multiple times and averaging the results. Over time the image should get better as the errors are diluted. It will significantly increase the amount of HPU time required, but with enough human processing units willingly taking part the wall-clock time might not be too badly affected.

Yes, I find it interesting to note the different types of errors. There are some random errors, but many of the errors seem to be repeated. It looks like a lot of people ended up in the wrong code path, resulting in blue/white pixels in the lower half, while fewer people made the reverse mistake (yellow pixels in the upper half). There are a lot of purple pixels in the upper right; I wonder what led many people to the same mistake.

Another interesting thing is to try to reverse-engineer the worksheet: section B is the sphere, section C is the ground, and section D is the sky. But then there's the lighting model, shadow, etc.

A lot of the magenta pixels are people thinking that ####|1 means "leave 1 digit" instead of "remove 1 digit"

All of the pixels were already taken by the time I tried, but I did an "error" pixel (11, 26) just for my own pleasure.

Somehow I got RGB(255, 50, 194), which is different from the value posted on the chart. Actually, I'm not sure how originally they got 0, since G comes from R and B, which are both positive, and the expression is multiplication and addition.

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