How does one tiny rule draw a giant, detailed snowflake?

This snowflake has bumps on bumps on bumps — more wiggles than you could ever draw by hand. But nobody drew them. There's just one tiny rule, repeated. Let's find that rule… then see how far it can go.

1What you need: a rule, and "do it again"

A rule is one instruction — repeating feeds it back into itself

You only need two ideas. Watch each one:

A tiny rule

One instruction: take a straight line and push a little tent up in its middle. One straight line becomes four shorter bent lines. That's the whole rule.

Do it again

The rule eats its own output. Every new short line is a line too — so you do the rule to all of them again. And again. Same rule, smaller and smaller.

2One line, two choices

Leave it alone, or use the tent rule

A straight line has two futures. This one little choice is the seed of everything that comes next:

Do nothing

Leave it alone

A straight line stays a boring straight line. Repeat "do nothing" forever and… it's still a straight line.

The tent rule

Tent the middle

Swap the middle third for a little tent: one line becomes four. Same rule, every time — but now there's something to repeat.

3Your turn — shape the rule

Make the tent flatter or pointier, just once

Here's a plain triangle with the tent rule done one time to every edge. Drag to change how pointy each tent is, and watch the same single rule make a fatter or sharper star.

one round of the tent rule on a triangle
How pointy is each tent?a gentle bump
FLATSHARP SPIKE

4Now repeat the same rule

Keep the rule. Just do it again and again. ❄️

Same tent rule, never changing. The only thing you'll change is how many times you repeat it. Guess first — then drag the repeats up and watch.

Guess before you drag

You take ONE simple rule and just keep repeating it on a plain triangle. After many repeats, the outline is…