# Homework #6

1. Make a Hutchinson map similar to the one for the Cantor set but using slightly different contraction mappings. Show that it is contractive on H(R), and discuss its invariant set.

2. Make a Hutchinson map similar to the one for the Sierpinski triangle but using slightly different contraction mappings (all with the same contractivity factor). Show that it is contractive on H(R2), and discuss its invariant set. Include a plot of the invariant set.

3. Make a Hutchinson map similar to the one for the Sierpinski triangle but using contraction mappings with unequal contractivity factors. Show that it is contractive on H(R2), and discuss its invariant set. Include a plot of the invariant set.

4. Make a Hutchinson map similar to the one for the Sierpinski carpet but using slightly different contraction mappings (all with the same contractivity factor). Show that it is contractive on H(R2), and discuss its invariant set. Include a plot of the invariant set.

5. Make a Hutchinson map similar to the one for the Sierpinski carpet but using contraction mappings with unequal contractivity factors. Show that it is contractive on H(R2), and discuss its invariant set. Include a plot of the invariant set.