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A brief detour through the Mandlebrot set

Before we dive into a more complicated DAG, let's get a more interesting job. I'm tired of this lazy, sleepy job that only does trivial mathematics. Let's make pretty pictures!

We have a small program that draws pictures of the Mandlebrot set. You can read about the Mandlebrot set on Wikipedia, or you can simply appreciate the pretty pictures. It's a fractal.

We have a simple program that can draw the Mandlebrot set. It's called goatbrot.

Downloading the needed executables

Since your training VMs don't have the goatbrot executable needed for this exercise, we will need to download it first. Execute the following commands to do this:

$ mkdir bin
$ cd bin
$ wget https://www.nhn.ou.edu/~hs/tmp/goatbrot
$ chmod +x goatbrot
$ cd ..

A simple invocation of goatbrot

You can generate the Mandlebrot set with two simple commands.

  1. Generate a PPM image of the Mandlebrot set:
$ ~/bin/goatbrot -i 1000 -o tile_000000_000000.ppm -c 0,0 -w 3 -s 1000,1000
  1. Convert it to a JPEG image and write into your home directory:
$ convert tile_000000_000000.ppm ~/mandle.gif

  1. We need to download the GIF file from your training VM to your local desktop. To do so, find the file mandle.gif in the list of files and directories in the side bar to the left of your terminal window. Right-click on it and select Download, and download it to your local desktop.

  2. Point Browser at the file URL: open a Terminal on your local CentOS VM, and then type in there:

firefox Downloads/mandle.gif

The goatbroat program takes several parameters. Let's break them down:

  • -i 1000 The number of iterations. Bigger numbers generate more accurate images but are slower to run.
  • -o tile_000000_000000.ppm The output file to generate.
  • -c 0,0 The center point of the image. Here it is the point (0,0).
  • -w 3 The width of the image. Here is 3.
  • -s 1000,1000 The size of the final image. Here we generate a picture that is 1000 pixels wide and 1000 pixels tall.

Dividing goatbrot up

The Mandlebrot set can take a while to create, particularly if you make the iterations large or the image size large. What if we broke the creation of the image into multiple invocations then stitched them together? Once we do that, we can run each goatbroat in parallel in our cluster. Here's an example you can run by hand. (This is back in your first terminal, where you are logged into the osgconnect machine.)

  1. Run goatbroat 4 times: 
$ ~/bin/goatbrot -i 1000 -o tile_000000_000000.ppm -c -0.75,0.75 -w 1.5 -s 500,500
$ ~/bin/goatbrot -i 1000 -o tile_000000_000001.ppm -c 0.75,0.75 -w 1.5 -s 500,500
$ ~/bin/goatbrot -i 1000 -o tile_000001_000000.ppm -c -0.75,-0.75 -w 1.5 -s 500,500
$ ~/bin/goatbrot -i 1000 -o tile_000001_000001.ppm -c 0.75,-0.75 -w 1.5 -s 500,500
  1. Stitch them together: 
$ montage tile_000000_000000.ppm tile_000000_000001.ppm tile_000001_000000.ppm tile_000001_000001.ppm -mode Concatenate -tile 2x2 ~/mandle.gif

This will produce the same image as above. We broke the image space into a 2 by 2 grid and ran goatbrot on each section of the grid. The montage program simply stitches the files together.

Try it!

Run the commands above, make sure you can create the Mandlebrot image. When you create the image, you might wonder how you can view it.

The same way we did above.
1. Find the file mandle.gif in your side bar again. 2. Download it and display it in Firefox.