What quantity did you change?
Labs / Mathematics
Mandelbrot Explorer
Every colored pixel asks the same question: starting from zero, does repeatedly applying z → z² + c stay bounded, or race off to infinity? Click to dive into the fractal boundary, box-drag to frame a region, and glide your pointer around to see the Julia set that belongs to the point c beneath it.
Labs / Mathematics / Mandelbrot Explorer
Mandelbrot Explorer
Every colored pixel asks the same question: starting from zero, does repeatedly applying z → z² + c stay bounded, or race off to infinity? Click to dive into the fractal boundary, box-drag to frame a region, and glide your pointer around to see the Julia set that belongs to the point c beneath it.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
center —zoom 1.0×n —
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Zoom into a fjord along the black boundary. Do the shapes ever stop repeating, or keep going forever?
- Drag the pointer just inside the black set versus far outside it. How does the Julia set's shape change?
- Zoom deep, then raise the max iterations. Why does new detail suddenly appear where there was only flat color?
- Hunt for a tiny black "mini-Mandelbrot" far from the main body. How much do you have to magnify to find one?
- Watch the cursor's iteration count as you approach the boundary. Why does it climb toward your max just before a point turns black?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
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.