Microfractal 🫖 (@[email protected])

Attached: 1 image An attempt to approximate a Basilica Julia set by zooming into the Mandelbrot set. The problem with a Basilica Julia set, however, is that this type of Julia is at the point -1 + 0i in the complex plane. This point will never exceed the escape radius, and is therefore part of the Mandelbrot set (interior). It follows that this Julia set also has parts of never escaping cycles, which makes finding an embedded Julia set impossible. However, it is possible to find an approximation of this shape by repeatedly zooming in from a periodic point (a point where a mini-Mandelbrot set can be found), relative to this point (and especially relative to it's rotation), to a point that is as close as possible, relatively speaking, to -1 + 0i. With many repetitions, this results in an approximately equal (but not perfect) image of the Basilica Julia set. This image shows the final stage after ~20 repetitions (this is also known as Julia morphing). #fractalart #fractal #mandelbrot #mandelbrotset #juliaset #image #art