Graphing in 3D
Many fractals, such as some strange attractors and quaternions require you to graph points in 3 dimensions. This is also necessary for creating 3-dimensional objects such as fractal landscapes. In order to display such fractals on the screen, you need to graph the 2-dimensional projection of the object. The most common way of graphing fractals on the screen is by making the z-axis vertical, x-axis horizontal, and the y-axis at a 45 degree angle in between them:
If you now take these axes and try to work out formulas for transferring the coordinates into 2 dimensions, you should be able to do so without using any knowledge other than the Pythagorean Theorem. Taking any point (x, y, z), use the formulas:
new_x = x + y / sqr(2)
new_y = z + y / sqr(2)
and then graph the point (new_x, new_y).