I am a fan of Arthur C Clarke, but this film left me unimpressed.
It's basically Mandelbrot porn, with Mandelbrot religion, and very little science or math.
How can they not explain that fractals are objects with fractional dimension? How can they not explain that "the plane" used is not the real plane, but the complex plane?
As far as fractal compression, they fail to explain that it's lossy compression, and the "detail" revealed by zooming in simply isn't there. It's like a painting where the painter makes up the detail. It may be a good guess, but it's not real.
I'm not sure I approve their use of the equilibrium symbol "⇌" in their equation z⇌z²+c. I think it's a confusing way to represent recursion, particularly with similarity to the equals sign. Although it's true that z→z²+c (z is mapped to z²+c), the heart of it is z←z²+c (z is replaced by z²+c), which is then repeated up to some arbitrary limit, for each pixel of interest. z is a coordinate in the complex plane, which is why you can square it. Squaring a real point in two dimensions doesn't make a lot of sense.
Fractals do not map well to reality. If you zoom in on the fractals shown in this film, you can theoretically keep zooming as far as you want, and it still looks the same. But one reason we have such difficulty with the tiny world of quarks and quantum mechanics is precisely because it's NOTHING like the world we know.
It's basically Mandelbrot porn, with Mandelbrot religion, and very little science or math.
How can they not explain that fractals are objects with fractional dimension? How can they not explain that "the plane" used is not the real plane, but the complex plane?
As far as fractal compression, they fail to explain that it's lossy compression, and the "detail" revealed by zooming in simply isn't there. It's like a painting where the painter makes up the detail. It may be a good guess, but it's not real.
I'm not sure I approve their use of the equilibrium symbol "⇌" in their equation z⇌z²+c. I think it's a confusing way to represent recursion, particularly with similarity to the equals sign. Although it's true that z→z²+c (z is mapped to z²+c), the heart of it is z←z²+c (z is replaced by z²+c), which is then repeated up to some arbitrary limit, for each pixel of interest. z is a coordinate in the complex plane, which is why you can square it. Squaring a real point in two dimensions doesn't make a lot of sense.
Fractals do not map well to reality. If you zoom in on the fractals shown in this film, you can theoretically keep zooming as far as you want, and it still looks the same. But one reason we have such difficulty with the tiny world of quarks and quantum mechanics is precisely because it's NOTHING like the world we know.