CS Unplugged activity

Pixel Pictures

About 30 minutesSolo, or trade with a partnerPencil

Every picture on a screen, every photo, every icon, every letter you’re reading right now, is made of tiny colored squares called pixels (short for “picture elements”). Zoom in far enough on any image and that’s all you’ll find: a grid of small, solid squares, nothing smoother underneath.

A computer can’t draw a soft curve by magic. It can only store numbers. So to store a picture, it needs a way to turn a grid of pixels into a list of numbers, and back again. This activity walks you through one simple way to do exactly that, for a picture that only uses black and white.

The rule

Look at one row of a black and white picture at a time, left to right. Instead of writing down the color of every single pixel, write down how many pixels you see before the color changes. Each one of those counts is called a run, and the list of counts for a row is its code.

The one rule that makes this work: the first number in a row’s code is always a count of white pixels. If a row actually starts with a black pixel, you still write the white count first, and it’s just 0.

For example, this five pixel row:

..###

has 2 white pixels, then 3 black. Its code is 2, 3.

This row also has five pixels, but starts black:

##...

has 0 white pixels (none, before the black starts), then 2 black, then 3 white. Its code is 0, 2, 3.

Add up the numbers in any row’s code and you should always get back the width of the picture (5, in both examples above). That’s a quick way to check your own work as you go: if a row’s numbers don’t add up to the grid’s width, you’ve made a mistake somewhere in that row.

Decode these pictures

Below are four pictures, written as codes instead of pixels. Each line of a picture’s code is one row, in order from top to bottom. Shade in the matching squares on the blank grid with your pencil, one row at a time. Leave a square blank for white, and shade it in solid for black.

Work through them in order. They start easy and get trickier.

Make your own, and trade

Now try it the other direction. Draw a small black and white picture of your own on the Your picture grid below. Keep it simple, nothing fancy, just solid black or white squares. Then write down its code, row by row, on the lines underneath, the same way you just decoded the pictures above.

Trade codes with a partner, or read yours out loud to someone nearby. Decode their code onto the Decode here grid, then compare grids square by square. Every square should match. If two of you disagree on a square, check that row’s numbers add up to 6 first; that’s where most mistakes hide.

Your picture

Decode here

Your code, one row at a time:

Thinking about compression

Writing a whole picture as a short list of numbers, instead of writing down all one hundred pixels one at a time, is already a kind of shortening trick. Computer scientists call this compression: storing the same information with less writing.

Look back at the four pictures you decoded. Which ones took the fewest numbers to write? Which took the most?
A picture that’s mostly one solid color compresses very well with this method: one big run needs only one number. Why does a picture that changes color on almost every pixel (like static on an old TV screen) compress badly, maybe even worse than just listing every pixel?
Suppose a computer could only write numbers up to 7 in a row’s code, no higher. How would you write a run of 12 black pixels? Hint: split it into two black runs, with a run of 0 white pixels in between them.

Want the harder version of this, with real numbers to work out? See Pixel pictures: how much do you save?.

Compression questions

Plus, Diamond, and Boat were all tied for shortest, 28 numbers each. Target took the most by far: 60 numbers, more than twice as many as the shortest pictures.
Every time the color changes, you need to start a new run, which means a new number. A picture that flips color on nearly every pixel needs almost as many runs as it has pixels, so its code ends up close to the same length as just listing every pixel, or even longer, since a run of length 1 still needs its own number.
7, 0, 5: a run of 7 black pixels, a run of 0 white pixels (because the next pixel is also black), then a run of 5 more black pixels.