x5

• or click above to zoom in by X times •

• or click above to zoom in by X times •

↓ (i)teration = 0

i = 1000 ↑

The Mandelbrot Set^{🔗} is a set of numbers that form a boundry and probably one of the most popular modern mathimatical images, and a thing of personal fascination when I learned of fractals as a kid in the 80's, when computers were just starting to become powerful enough to render them at home. In honor of the passing of Benoit Mandelbrot, in 2010, I created this demo, which rendered his famous fractal. I'm continously returning to the code to add new features... and to delve into the fractal.

Each pixel is evaluated to see if it lies within the set. Over repeated iterations, it checks to see if the value remains reasonable or explodes in value. The gradient represents degrees of when it exploded. Each pixel is simply a value of 0 to the maximum number of iterations calculated... in this case it's 1000 times. Color comes from creating different palettes for what those 0-1000 values should be. The bulk of the fractal is where it was stable after all iterations, outside where it exploded very early. However, it's the boundry of stability and exploding into infinity where it gets really interesting. To infinity, and beyond!

Use the controls to zoom in and zoom out, as well as reset back to the original. You can also click anywhere on the visualization to zoom in centered at that spot. You can save a full-sized PNG of the rendered image by clicking on the camera above and then right-click and save the thumbnail. If you are on a phone, press and hold the thumbnail after tapping the camera. An 800x500 PNG will be saved.

Using a x2 level per zoom, zoom in 50 times. That's 2^50... or a zoom level of x1,125,899,906,842,624! At around 46 times you can start to see JavaScript's floating point limit and by around 56 times you are lost within your computer's absolute computational limit. You just pushed your browser to the very edge of infinity and it blew its mind.

Each pixel is evaluated to see if it lies within the set. Over repeated iterations, it checks to see if the value remains reasonable or explodes in value. The gradient represents degrees of when it exploded. Each pixel is simply a value of 0 to the maximum number of iterations calculated... in this case it's 1000 times. Color comes from creating different palettes for what those 0-1000 values should be. The bulk of the fractal is where it was stable after all iterations, outside where it exploded very early. However, it's the boundry of stability and exploding into infinity where it gets really interesting. To infinity, and beyond!

Use the controls to zoom in and zoom out, as well as reset back to the original. You can also click anywhere on the visualization to zoom in centered at that spot. You can save a full-sized PNG of the rendered image by clicking on the camera above and then right-click and save the thumbnail. If you are on a phone, press and hold the thumbnail after tapping the camera. An 800x500 PNG will be saved.

Using a x2 level per zoom, zoom in 50 times. That's 2^50... or a zoom level of x1,125,899,906,842,624! At around 46 times you can start to see JavaScript's floating point limit and by around 56 times you are lost within your computer's absolute computational limit. You just pushed your browser to the very edge of infinity and it blew its mind.