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Julia sets and the Mandelbrot set

Many folks here know of the Mandelbrot set which has been implemented here on Observable, where the emphasis is on interactive exploration of the set by panning and zooming. The Mandelbrot set arose, though, as an attempt to understand more fundamental objects called Julia sets. I recently posted my take on exploring the relationship between the Mandelbrot set and Julia sets:

Rather than zooming, this notebook allows you to click on the Mandelbrot set to generate the corresponding Julia set. You can then hover over the Julia set to visualize the orbit of the selected point. Thus, you end up generating pictures that look like so:


Extremely cool!

I’ve just sent you a teeny suggestion, allowing you to drag across the Mandelbrot representation to re-draw the Julia set. It renders plenty fast!

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Thanks! Merged and re-published.

I had considered doing that on mouse move but hadn’t considered a drag like that.


I was playing with this a bit more this morning and noticed that it had been added to Obersvable’s Explorables Collection. I was wondering if you put it there? If so, that’s totally awesome and thanks! I’m just curious about the mechanism by which that happens - if, for example, it’s automated or if there’s a few specific folks involved in the selection.

I did!

Speaking generally, the Observable team doesn’t have special powers within the Observable app — but one of the few things any of us can do is add notebooks to the default collections featured on the Explore page.

They’re a little less visible now than they used to be: they previously were constant content on the home page.

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