What are complex fractals?

Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

Is the Mandelbrot fractal infinite?

The boundary of the Mandelbrot set contains infinitely many copies of the Mandelbrot set. In fact, as close as you look to any boundary point, you will find infinitely many little Mandelbrots. The boundary is so “fuzzy” that it is 2-dimensional.

Why is the Mandelbrot set so complex?

The Mandelbrot set is the set of complex nmbers c such that the sequence 0, qc(0)=c, qc(qc(0))=c2+c, qc(qc(qc(0)))=(c2+c)2+c,… remains bounded. That is the reason why you see that complex behaviour when zooming up on a small region.

What is the most famous fractal?

the Mandelbrot set
Largely because of its haunting beauty, the Mandelbrot set has become the most famous object in modern mathematics. It is also the breeding ground for the world’s most famous fractals.

Is butterfly fractal?

The Hofstadter butterfly is a fractal pattern—it contains shapes that repeat on smaller and smaller size scales. In fact, the Hofstadter butterfly is one of the first quantum fractals theoretically discovered in physics but, until now, there has been no direct experimental proof of this spectrum.

Is the universe a fractal?

The universe is definitely not a fractal, but parts of the cosmic web still have interesting fractal-like properties. For example, clumps of dark matter called “halos,” which host galaxies and their clusters, form nested structures and substructures, with halos holding sub-haloes and sub-sub-halos inside those.

Is the Fibonacci spiral a fractal?

The Fibonacci Spiral, which is my key aesthetic focus of this project, is a simple logarithmic spiral based upon Fibonacci numbers, and the golden ratio, Φ. Because this spiral is logarithmic, the curve appears the same at every scale, and can thus be considered fractal.