AoC 2017 Day 21: Fractal Expander

Source: Fractal Art

Part 1: Start with an input image made of . and # pixels. For n iterations, break the image into blocks:

  • If the current size is even, break the image into 2x2 chunks and replace each with a 3x3 chunk
  • If the current size is odd, break the image into 3x3 chunks and replace each with a 4x4 chunk

The replacement rules will be specified in the following format (example is a 3x3 -> 4x4 rule):

.#./..#/### => #..#/..../..../#..#

In that example, replace this:

.#.
..#
###

With this:

#..#
....
....
#..#

Any rotation or reflection of a chunk can be used to match the input of a replacement rule.

After n = 18 iterations, how many # pixels are there?

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Mandelbrot

Perhaps the best known fractal of all: the Mandelbrot set.

Since I was already working on Python code that would render an image given a function (for a future post), I figured that I might as well render fractals with it.

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Clockception

Let’s talk about clocks.

We can draw traditional analog clocks1:

We can draw nice digital clocks:

┌─┐  │ │ ─┐ ┌─┐
│ │└─┤    │ │ │
└─┘  │ │ ─┴─└─┘

Or we can go downright mad and make clocks out of clocks:

Even animated!

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Regular Expression Fractals

Oops, turns out I haven’t had a post in a good long while. Before it gets even longer, I figure that I should take one off my backlog and just write it up, even if it is a little on the shorter side.

Today’s post was inspired by this post on /r/dailyprogrammer a month ago today: Challenge #178 [Hard] Regular Expression Fractals. The basic idea is that you are going to take a rectangular region and divide it into four quadrants, again and again, recording the path as you go (images from that post):

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Fractal Invaders

Today’s post is a follow up to Sunday’s post Procedural Invaders. This time around, we’re going to work through two different space filling algorithms in order to eventually generate something like this:

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