Hunting The Hidden Dimensions – Fractals (part 1 of 4)

Spent the last hour watching this

Well worth it, especially the Antenna segment.

CrazyNeutrino said:

Hunting The Hidden Dimensions – Fractals (part 1 of 4)

Spent the last hour watching this

Well worth it, especially the Antenna segment.

Just started watching. A couple of initial comments.

1) Producing a realistic simulation of mountains was a primary aim of Mandelbrot’s initial work, rather than a later add-on.

but

2) Saying that it was “dead simple” to simulate mountains using fractals makes me shudder. I personally, as part of my work on wind flow over mountainous terrain, and before fractal mountains became the mainstay of computer games, tried to use Mandelbrot’s fractals to generate some realistic mountains. Despite my best efforts, what I came up could best be described as “awful”. If it was “dead simple” to the narrator then he must be a genius.

Perhaps I can explain better by saying this. The Weierstrass curve is a fractal that looks a bit like a mountain, but it is not a realistic mountain shape. It’s also 2-D. Every 3-D fractal that I came up with that looked a bit like a mountain wasn’t a realistic mountain shape. By dint of great effort I came up with one that looked a little bit like a real mountain. What you have in even the most basic 3-D computer game looks almost infinitely better than what I ended up with.

mollwollfumble said:

CrazyNeutrino said:

Hunting The Hidden Dimensions – Fractals (part 1 of 4)

Spent the last hour watching this

Well worth it, especially the Antenna segment.

Just started watching. A couple of initial comments.

1) Producing a realistic simulation of mountains was a primary aim of Mandelbrot’s initial work, rather than a later add-on.

but

2) Saying that it was “dead simple” to simulate mountains using fractals makes me shudder. I personally, as part of my work on wind flow over mountainous terrain, and before fractal mountains became the mainstay of computer games, tried to use Mandelbrot’s fractals to generate some realistic mountains. Despite my best efforts, what I came up could best be described as “awful”. If it was “dead simple” to the narrator then he must be a genius.

Perhaps I can explain better by saying this. The Weierstrass curve is a fractal that looks a bit like a mountain, but it is not a realistic mountain shape. It’s also 2-D. Every 3-D fractal that I came up with that looked a bit like a mountain wasn’t a realistic mountain shape. By dint of great effort I came up with one that looked a little bit like a real mountain. What you have in even the most basic 3-D computer game looks almost infinitely better than what I ended up with.

Does it look like a newly formed (relatively speaking) mountain without weathering and erosion or even without those missing components no.

Cymek said:

mollwollfumble said:

CrazyNeutrino said:

Hunting The Hidden Dimensions – Fractals (part 1 of 4)

Spent the last hour watching this

Well worth it, especially the Antenna segment.

Just started watching. A couple of initial comments.

1) Producing a realistic simulation of mountains was a primary aim of Mandelbrot’s initial work, rather than a later add-on.

but

2) Saying that it was “dead simple” to simulate mountains using fractals makes me shudder. I personally, as part of my work on wind flow over mountainous terrain, and before fractal mountains became the mainstay of computer games, tried to use Mandelbrot’s fractals to generate some realistic mountains. Despite my best efforts, what I came up could best be described as “awful”. If it was “dead simple” to the narrator then he must be a genius.

Perhaps I can explain better by saying this. The Weierstrass curve is a fractal that looks a bit like a mountain, but it is not a realistic mountain shape. It’s also 2-D. Every 3-D fractal that I came up with that looked a bit like a mountain wasn’t a realistic mountain shape. By dint of great effort I came up with one that looked a little bit like a real mountain. What you have in even the most basic 3-D computer game looks almost infinitely better than what I ended up with.

Does it look like a newly formed (relatively speaking) mountain without weathering and erosion or even without those missing components no.

Thanks for asking :-)

It looked like this. The vectors are wind flow turbulence in the lee of the mountains.

Not anywhere near as nice as fractal mountains in computer games.

Looking up links from “fractal landscape” leads to a dead end search (simplex noise) an infinite loop (fractal landscape -> scenery generator -> fractal landscape). The only method actually described in Wikipedia is https://en.wikipedia.org/wiki/Diamond-square_algorithm and, to be fussy, that isn’t a fractal. It’s a multi-step random generator.

Even then, the original Diamond-square algorithm was flawed, and needed to be fixed in a generalized algorithm introduced by J.P. Lewis. In this variant the weights on the neighboring points are obtained by solving a small linear system motivated by estimation theory, rather than being fixed.

As I say, very non-trivial.