Mandelbrot set: for $z, a\in \mathbb C$, define $f_z(a)=a^2+z$, and $f_z^{(n)}(a) = f_z \left( f_z \left( \cdots f_z(a) \cdots\right) \right) $ where $f_z$ is applied $n$ times. Given a threshold $M\in \mathbb R^+$, for each $z=x+yi\in \mathbb C$, compute the smallest $n$ such that $\bigm|f_z^{(n)}(0)\bigm| > M$, and assign the color at coordinates $(x,y)$ according to the value of $n$. And Voila!

Below you can switch between Mandelbrot and Julia sets. You can adjust the size, the maximum number of iterations, the threshold $M$, the coloring scheme, and the color palette. In case of Julia set, you can also click on the gray square to change the value of $w$. The computation runs in your browser, be patient, it may take a few sections after you release the slider for the image to update, if you use CPU compute. (Tip: smaller image size runs faster, WebGL is much faster than CPU.)

Double click on the image to zoom in. Double click while holding "Shift" key to zoom out. Drag the image to move.

$w=$
Image Size :
900*600
 Max Iterations:
4500
 Threshold $M$ :
4
 Color Palette :
0