Fractals in Movies, Game design and Engagement

[kram1032]

In this episode of Extra Creditz, they explain the typical engagement curve, found in all sorts of successful movies and games. I've seen that already, but:
They also point out how these engagement curves apply on all time-scales. That sort of surprised me and reminded me once again, how fractals are literally everywhere.
Enjoy!
<a href="https://www.youtube.com/v/5LScL4CWe5E&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/5LScL4CWe5E&rel=1&fs=1&hd=1</a>

(By the way, on an unrelated sidenote, in recent times, I've found various such examples of fractals in the world and always shared them here but they barely get any attention at all. I'm feeling like the "huge lack of comments" does not only apply to the pretty works of the community. It applies to the entirety of the forums... /rant)

[eiffie]

Yeah the engagement curve is pretty flat here at times but I really enjoy your links. Sometimes I follow them and get lost for months.

[kram1032]

Good to know that what I'm doing isn't entirely pointless

[Chillheimer]

Sorry for pulling this old one up, but I wanted to underline that it is not pointless!
I'm on a big hunt for more fractals in life, especially the ones that aren't so obvious, or not to be seen with the eye.
I found your link interesting and funny, thanks for posting! One more added to the list.

I actually think that your rant doesn't go far enough.. the whole world, especially "the scientists" don't pay enough attention to the answers that fractals might give them. (I see it like the possibility to view things from 2 different angles, whereas scientists voluntarily limit themselves to just one view.)

regards!

[kram1032]

Actually, I get the impression that scientists often are very interested in fractals.
The problem is, that fractals, as trivial as the basic concept may be (repeated function application => pretty patterns), are in many ways not very accessible with our current mathematical tools.
On an analytic side of things we basically hit a wall that is difficult to overcome.

Though technically, any physics simulation we do on computers today works via iterative refinement and, if you choose the right initial conditions, will pretty much always cause some kinds of fractal patterns.

There are certain field of analyis that deal with iterated functions and lead to interesting things like the
functional square root which gives you the function you need to apply twice in order to get the function you put in, analogous to the squareroot of a number being the number you need to multiply with itself to get the number you put in.

Basically you could define any functional power and from there a functional exponential and similar things. It's just really difficult to get any results at all.
What we'd need is some kind of breakthrough. Then, there will suddenly be a whole lot more attention on the research side.
But beyond fairly trivial cases, all of those are very involved.

Edit: More generally, you have so-called Superfunctions

Edit 2: The biggest "problem" is that what we actually have solutions for usually are the least interesting bits of fractals.
Fixed points and divergent behaviors.
Those are comparatively uninteresting because they are simple and predictable. That very predictability makes them easy to solve.
However, what makes fractals visually stunning usually is the chaotic sections that can look great and repeat indefinitely in some weird non-trivial but clearly existing symmetry. That's where methods we already have often fail. Methods other than the iterative ones, at least.
Iterative methods are great for numeric solutions. Computers can handle them easily. In that form, fractals (or systems that contain fractal behavior) are calculated and used pretty much everywhere.