The Share button (bottom right, with Save at the bottom left, in the single-window views) makes an image of what you are looking at (at most twice the display size, so it is quick to make and easy to send) and opens your device's share sheet so you can send it to someone. The message includes a link. Anyone who opens the link sees the same fractal in this program, with the same type, power, position, zoom, rotation, and colors. On a computer without a share sheet, Share copies the link and offers to save the image instead. Links only work when this page is opened from a web address, not from a file on your computer.
The selector at the top left chooses the fractal. Mandelbrot is the classic set: repeat z → z² + c starting from z = 0. Nova is a Newton fractal: each step applies Newton's method for z³ − 1 and then adds c, z → z − (z³ − 1) / (3z²) + c, starting from z = 1 (one of the three roots of z³ − 1).
In Nova, a point is colored by how quickly the steps settle down to a fixed value, and it is black if they never settle within the iteration limit. With Nova selected, Julia shows the Nova Julia set for the c you choose (c = 0 gives the classic Newton fractal), and Orbits shows the path that starts at z = 1 and is pulled toward the roots.
The Power button opens a slider for the exponent: the d in z → zd + c for Mandelbrot, and the p in Newton's method for zp − 1 for Nova. Drag it anywhere from 1 to 9 (at 1 the Mandelbrot rule z → z + c always escapes, so almost nothing is left of the set). Whole numbers give the classic higher-power sets (4, for example, has three-fold symmetry), and the values between them morph smoothly from one set to the next, with a faint seam along the negative axis where a fractional power is not single-valued. The slider eases onto each whole number so it is easy to land on one, but only within a few pixels, so values just beside a whole number stay within reach. The arrow keys move it in steps of 0.01 (0.1 with Shift) when it has focus. Fractional powers take more computing, which is quick on your graphics chip but slower once you zoom deep enough for the precision renderer to take over.
Zoom, pan, rotate, Save, the keyboard shortcuts, and all the color controls work the same for both. Switching type resets the view, and each type remembers its own c, Power and Iterations setting.
The same palette colors the orbit, stepping through it from the first point to the last, and one eighth of the Density setting sets how many times it repeats along the way. Julia opens a second window showing the Julia set for the point c you choose in the Mandelbrot set. Orbits shows the path that point takes when you repeat the Mandelbrot rule, with the same path traced faintly over the Mandelbrot set. Julia and Orbits can be on at the same time: the second window then shows the Julia set, and the orbit is drawn over both the Mandelbrot set and the Julia set. Press a button again to turn that mode off; when both are off, you are back to the Mandelbrot set alone. The enlarge icon (four corner marks) at the top right of the second window enlarges it to fill the screen, and pressing it again returns to two windows. Tapping or clicking a window never changes the view. The ? button is available in the Mandelbrot-only view and whenever Julia is on, but is hidden while Orbits is on by itself; turn Julia on or Orbits off to bring it back.
In the two-window view, the lock icon at the bottom left of the Mandelbrot window freezes c: the Julia set and orbit stay as they are while you zoom and pan the Mandelbrot set freely (one finger now pans instead of choosing c). Press the lock icon again to unlock, and c follows your pointer or finger again. Returning to the Mandelbrot set alone also unlocks c.
In an enlarged orbit, Animate grows the orbit one step at a time, and the slider sets how many steps to draw. In the Mandelbrot-only and enlarged views, Save downloads the image (or opens your device's share sheet), and the copy button next to it copies a link to the current view. The grid, coordinates, and zoom readout are never part of a saved image.
Each point c on the plane is tested with one rule: start at z = 0 and repeat z → z² + c. If z stays bounded forever, c is in the Mandelbrot set and is drawn black. Otherwise z escapes, and the color shows how many steps that took.
Every c also has its own Julia set. It uses the same rule, but c is held fixed and the starting z varies across the plane. Choose c inside the Mandelbrot set and its Julia set is one connected piece; choose c outside and it shatters into dust. The most intricate Julia sets come from c near the edge.
An orbit is the sequence z₀ = 0, z₁, z₂, … for one c. Inside the set it settles toward a point or loops through a cycle; outside, it flies away.
For Nova, c plays the same role as in the Mandelbrot set: the Nova "Mandelbrot" view maps every c, using the starting point z = 1, and each c has its own Nova Julia set where the starting point varies instead. Mini copies of the Mandelbrot set appear along the boundaries of the Nova view.
Speed and precision: shallow zooms are drawn by your graphics chip. Once you zoom past a few thousand times, the explorer switches to a slower but more precise renderer (badge at the top of this panel), which keeps working to about 10¹² times, the limit of standard double-precision numbers. Saved images are rendered at full quality either way.