What information entered the process?
Labs / Computer Science
Recursion
A recursive shape is defined in terms of smaller copies of itself. Pick a fractal, drag the depth slider, and watch the same rule apply again and again — each level drawn from tinier versions of the whole. Leave “grow level by level” on to see the recursion actually unfold, with the newest frontier picked out in orange.
Labs / Computer Science / Recursion
Recursion
A recursive shape is defined in terms of smaller copies of itself. Pick a fractal, drag the depth slider, and watch the same rule apply again and again — each level drawn from tinier versions of the whole. Leave “grow level by level” on to see the recursion actually unfold, with the newest frontier picked out in orange.
Why it matters
Why explore this?
Computer science turns clear rules into reliable processes. This model lets you step through those rules and see how each decision changes the result.
Explore
Try the model
depth 0 / 81 branches
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Bump the tree's depth up one step at a time. How many new branches appear each time — and why does the count roughly double?
- The Koch snowflake's outline gets longer at every level. Could its perimeter keep growing forever while the shape stays inside a small circle?
- Set the branch angle near 90° and then near 5°. What real plants do the extremes remind you of?
- Drop the length ratio to 0.4, then raise it toward 0.85. Where does the tree stop looking like a tree, and what does that say about the base case?
- In the Sierpinski triangle, every solid triangle hides three smaller ones. If you could zoom in forever, would you ever reach a piece that is not a triangle?
Explain
Make sense of what happened
Trace the process one step at a time. Name the rule used at each important step, then explain why the final result follows from those rules.
Check
Before you leave
Which rule changed it?
Why did the process produce this result?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.