Begin by inputing a starting IFS and a final IFS ('Start Pattern' and 'End Pattern'). That is, the 6 numbers a,b,c, d,e,f that define each of the transformations w_i of the initial and final IFS. You can either use the drop down menu to input the numbers for you, or you can input them yourself. Note: if you input them yourself then you must also specify the probabilities p for each transformation (one reasonable choice for the p's is just 1/k for each, where k is the number of transformations in the IFS). There can be up to 8 transformations w_1,...,w_8 for each IFS. On the left half of the blue screen is the fractal and on the right half of the blue screen is the blue print of the IFS that draws that fractal. At each iteration the fractal dimension of the fractal is computed and displayed (via box counting method with 3 grid sizes and a least squares fit).

The number of steps is initially set for 100, but you can change this yourself. Lowering this number will speed up the movie, but will make it more jumpy. Increasing this number will make the movie run smoother, but will slow it down. The number of iterations is initially set at 10,000 but you can also change this. Lowering this number will speed up the computations, but will make the fractals fainter. Increasing this number will make the fractals more filled out with points, but will slow down the computation. Finally, input whether you want the linear or trigonometric interpolation ('choose a function') - this interpolates between the initial and final IFS data: a(t) = t*a_f + (1-t)*a_i for the linear interpolation, and a(t) =a_i*[cos(t*pi/2)]^2 + a_f*[sin(t*pi/2)]^2 for the trigonometric interpolation, where a_i is the a-value of the initial IFS and a_f is the a-value of the final IFS. Similiar formulae for the other parameters b,c,d,e,f. If N is the number of steps, then t =M/N for M=1,2,...,N. At each step t, the Chaos Game is run to 10,000 iterations (or whatever you choose the number of iterations to be) to draw the fractal.

To start, click on 'Forward'.