[Video] Luis Riera on LinkedIn: #mandelbulb #math #art | 27 comments (2024)

An Ecuadorian-inspired MandelbulbI oftentimes marvel at the beauty of math and its intersection with art. I also marvel at how much I have yet to learn and understand about math - it's infinite.In school we mostly learn the basics like arithmetic, algebra, geometry and if we study further we might get to calculus and possibly some form of topology, differential geometry. Maybe abstract geometry, abstract algebra, geometric algebra or algebraic geometry. How about some number theory, combinatorics, complex analysis, harmonic analysis, or fractal geometry.The diverse expressiveness and ubiquitous appearance of math in every area of human endeavors has always attracted me towards it.Although I don't completely understand fractals, I am learning more about them. Fascinating how symbolic representations of abstract ideas can produce such subjectively cool entities. The Mandelbulb seen in this video, is a 3-D fractal. The general formula for the Mandelbulb isn't complicated on the surface:z_n+1 = (z_n^8) + cThe variable z_n is supposed to represent a 3-D extension of a complex number. Due to some mathematical difficulties with this, the Mandelbulb isn't a TRUE 3-D fractal extension of the Mandelbrot set, but it is an interesting shape to say the least.At a high level, the equation serves as a comparative mechanism which allows the complex geometry to take shape (pun intended). Depending on the output of the Mandelbulb formula, the corresponding input coordinates (x, y, z) are given a binary true or false value. For this particular case, any output value less than a threshold (bounded) is given a true value (aka it is rendered/shown on the screen). Otherwise, it is not shown. By changing the value of the exponent, the shape can be made to evolve through time and produce very complex morphing fractal animations.I then added a little splash of Yellow, Red, and Blue in honor of the Ecuadorian flag - since I'm not aware of many "Ecuadorian thought leaders/artists" in the public sphere. It is always good to not forget where we come from and what makes us unique.P.S. If you are looking to collaborate on an artistic or technical project - reach out and let's see if there is any overlap in interests 👍 Rendered using Blender.Music: Globular - To The Other Side Of Fractal Phase Space#mandelbulb #math #art

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