Month: April 2021

Posted on

Highlander 2

This must have been a very strange movie to make.

Edit 1: It continuously gets worse. Time travelling alien prison was a high-point.

That isn’t a statement often said.

Edit 2: I didn’t understand. I read the plot synopsis and thought it was terrible. I thought the plot was why it was terrible.

The plot is the best part.

Edit 3: In the future, OSHA doesn’t exist.

Edit 4: Okay seriously, that didn’t even register.

Posted on

Logistics Map 2

Following this.

So the leading digit graph looks pretty much the same between 10 iterations and 10,000. The double leading digit graph doesn’t. Is that a resolution issue or indicative of some deeper, underlying property?

Let’s do a million iterations, for 1,000,001 values of x.

The double leading digit graph looks fairly similar to the n=10,001 graph.

But there’s a catch.

The 11423 (a) iteration yielded x = 0.5 due to truncation error.

The next time that happens is n=44063. (b)

It happens again at 79519. (c)

(c-a)/(b-a) =|= 2

Inception noises.

Posted on

Logistics Map

Want to see something weird?

The Logistics Map is the iterative function: xn+1 = a*xn*(1-xn) where xn is some number between zero and 1, non-inclusive, alpha is a number between zero and 4, and xn+1 is the number you get when you do the math on xn.

So pick an x value arbitrarily: 0.6. x1 = 0.6

Pick alpha arbitrarily: 3.56995. alpha = 3.56995.

x2 = 3.56995 *0.6 * (1-0.6) =3.56995*0.6*0.4= 0.854388

That’s xn+1. xn in this case is x1. Think of xn+1 as being the next x. So you have a first x, 0.6, and the next x is 0.854388, and the next x is 0.438041158193768.

I picked the alpha because the numbers are highly chaotic and don’t go outside (0,1). The parenthesis means 0 and 1 are not included.

Then, for funsies, I bin the leading digits. So x1 is 6, x2 is 8, x3 is 4, etc. Zeros are never leading digits, so if a number was 0.0002, the leading digit would be 2. For extra funsies, I do the same for the first two digits below. (The images are named after the number of times I go through the function, so they’re 10s +1)

This is the plot of the first 11 values:

Okay, so what?

This is the first 101 values:

This is the first 10,001:

The shape doesn’t change. Oh, it squiggles a little. Here’s the first 4:

Other than resolution improvements, the shape remains basically the same for the leading digit graph. Does it do that for the double leading digit graph?

Posted on

Fantasy Gun

A lot of fantasy runs into problems because if the work follows the rule of cool, and guns are possible, then guns are cool.

But guns aren’t just cool but really useful, so everyone should be using the Power of Gun to solve their problems instead of Po Sword, Po Magic, Po Whatever.

And then you’re back at westerns. If the work doesn’t want to be a western but does want cool guns, that’s a dead end.