Mandelbrot and Julia explorer guide.
Two images use the same rule, z → z² + c. In the Mandelbrot view each pixel supplies c and starts z at zero. In the Julia view each pixel supplies the starting z and shares one selected c.
Download the Seahorse Valley view
Find Seahorse Valley
Open the explorer and select Seahorse Valley. The left view centers near −0.7463 + 0.1102i. Its horizontal width is 0.065 units. You can also import the downloaded view using Open view.
Choose a point near one of the spiral edges. The Julia view immediately uses that point as c. Click another nearby point or change only the imaginary part by 0.001. Watch the filtered bands at the boundary and how some dark regions separate into thin branches.
Compare the same point at two depths
Try 80 iterations, then 340 without changing c. An escape-time image colors points according to how soon the orbit can be shown to diverge. Dark pixels stayed within the escape bound for the chosen number of iterations. More iterations can reveal detail near the boundary, but a finite test cannot establish that every dark point stays bounded forever.
For c = 0 the filled Julia set is the closed unit disk. Points inside the circle stay bounded and points outside eventually escape under repeated squaring. Enter 0 for both coordinates to compare this simple case with the boundary at Seahorse Valley.
Save a view someone else can reproduce
Use PNG to export one rendered image. Use Save view JSON to keep both centers, zoom widths, the chosen value of c, and the iteration limit. A view file can be opened on another device.
Read more about the recurrence and escape-time coloring in MathWorld’s Mandelbrot set reference.