Connected basin · c = 0
Here z becomes z² on every iteration. The filled Julia set is the unit disk: a useful starting point before exploring more complicated boundaries.
Three places to begin
Rabbit branches · c ≈ −0.123 + 0.745i
Look for three main lobes and repeating branches. Small changes in c can reshape these connections even while the set remains connected.
Scattered islands · c = 0.5 + 0.5i
This parameter lies outside the Mandelbrot set. Its Julia set breaks into disconnected pieces; the finite rendering shows the larger islands.
How Mandelbrot and Julia are connected
Both views use the quadratic iteration z → z² + c. The Mandelbrot view varies c and starts at z = 0; each Julia view fixes c and varies the starting point z. Choosing a point on the first view selects the constant for the second.
For this quadratic family, a parameter in the Mandelbrot set gives a connected Julia set; a parameter outside gives a disconnected one. Colours show how quickly points escape within a finite iteration limit, so fine boundaries may need a closer look.
What changes in Phoenix mode?
Phoenix adds a memory term from the previous iteration. Here the selected point controls that memory parameter p, while the two Phoenix sliders control c. The Mandelbrot connection described above applies to Julia mode; it does not classify this Phoenix family.
Navigate on a phone or desktop
Tap or click the parameter plane to choose a point. Both views stack vertically on a small screen; use either Enlarge button to inspect a single view, then Show both views on the same button to compare again. Open Controls for presets and colours. Enable Interact to pinch or wheel to zoom; turn it off to return to page scrolling. Fullscreen keeps your current selection. On a computer, scroll over the parameter plane to zoom, and use W, A, S and D to nudge the selected point.
Continue exploring
Read the Julia set guide, compare the Mandelbrot mathematics, or explore Phoenix fractals. For deeper navigation visit Mandelbrot Deep Zoom; for moving detail try Julia Particle.