I’m a children’s musician and college algebra instructor working on a late-in-life iOS Dev career change. First project: a different kind of calendar for my dementia-challenged elderly mom.
Location
Stillwater, Oklahoma, USA
Education
Master's in Mathematics
Pronouns
he/him
Work
Adjunct Instructor, College Algebra; Children's Musician
Hey, Michael & Piko, I know a little about fractals from my mathematics background. A fractal is a shape with a fractional dimension. Whereas a line fills one dimension and a plane fills two dimensions, a fractal is infinite and takes up an infinite amount of space in a sense, but doesn't fill the entire dimension it's embedded in. So for example the one you posted there takes up part of a plane, but not the whole plane, since it's lacy and leaves a lot of fancy gaps and holes (typically only the points colored black are actually part of the fractal). So its dimension is a number somewhere between 1 and 2. That number is independent of scale, so no matter what small piece of the plane you look at, the fractal takes up that same proportion of the available space. In other words no matter how far you zoom in, you'll see the same level of detail. Fractals are generated by iterative processes and display certain properties, such as repetition of similar structures at vastly different scales. Anyhow, I think your gif is part of the Mandelbrot Set. That's something on my list of apps to make - an app that teaches about the Mandelbrot Set. It's mind-blowing how simple it is to generate, compared with the complexity of the resulting shape. Endlessly fascinating.
I'm a friendly, non-dev, cisgender guy from NC who enjoys playing music/making noise, hiking, eating veggies, and hanging out with my best friend/wife + our 3 kitties + 1 greyhound.
Hey, Michael & Piko, I know a little about fractals from my mathematics background. A fractal is a shape with a fractional dimension. Whereas a line fills one dimension and a plane fills two dimensions, a fractal is infinite and takes up an infinite amount of space in a sense, but doesn't fill the entire dimension it's embedded in. So for example the one you posted there takes up part of a plane, but not the whole plane, since it's lacy and leaves a lot of fancy gaps and holes (typically only the points colored black are actually part of the fractal). So its dimension is a number somewhere between 1 and 2. That number is independent of scale, so no matter what small piece of the plane you look at, the fractal takes up that same proportion of the available space. In other words no matter how far you zoom in, you'll see the same level of detail. Fractals are generated by iterative processes and display certain properties, such as repetition of similar structures at vastly different scales. Anyhow, I think your gif is part of the Mandelbrot Set. That's something on my list of apps to make - an app that teaches about the Mandelbrot Set. It's mind-blowing how simple it is to generate, compared with the complexity of the resulting shape. Endlessly fascinating.
Wow, thanks for this detailed explanation, Monty! This is helping me to understand.
Also, cool idea around creating the app that teaches about the Mandelbrot Set... I'd love to check that out!