Sierpinski Carpet Project

You will be creating a sierpinski carpet fractal as shown below:

The approach to this project is very similar to the sierpinski gasket triangle example (called gasket2) from the textbook code. The fundamental difference here is we are not thinking about triangles, but squares instead. Much like the triangle, we start with one large square, and then consider what parts of the square need to be drawn, and which are discarded. To do this, each call to divide square must break up the square into 8 equal squares. We don’t keep the center square, as that is discarded. The recursion then takes place on each of the subsquares.

It may help to visualize the process with this illustration.

To help with the fractal, you many want to:

• Use the mix(a, b, s) function from MV.js interpolates a new vector based on a and b, and a scaling factor
  • Where a and b are vectors and s is a scaling factor
  • See the gasket2 example from the textbook code for a usage example
• Be very careful with your vetices with respect to their order and the relationships betwen them when you subdivide
• Careful, your render function will be different due to the TRIANGLE_FAN to make a sqaure

Your starter code will be the gasket2 example from the Textbook. You will need to modify the code to make it work for this project.

Grading

You will earn up to 30 points for this exercise, broken down as follows:

• 10 points - Output fractal matches sample image exactly
• 2 points - The size of the fractal must be 2 x 2
• 5 points - All squares are created using gl.TRIANGLE_FAN and FOUR vertices
• 5 points - Fractal subdivision must be a recursive function named divideSquare
• 4 points - A supporting function named square will take four vertices and add a square to the list of vertices to be drawn
• 3 points - The fragment shader must be used to color the squares
• 1 point - The background must be black