Mandelbrot Set Extra Credit Project
Due 9/17/2015
Name ________________________
Date ____________ Pd _________
This is an extra credit assignment. Therefore, I will not accept it from you unless
you have all of your quizzes and tests done, and I will not accept it late. This is
an all or nothing grade: you need to do a good job on I, II, and III, and you need
to answer the question in part IV to the best of your ability to get full credit. It
will be worth a 10% boost on a test. Good luck!
I.
Draw real and imaginary axes on a sheet of
graph paper, numbering maybe -5 to 5, counting
by quarters or halves. (If you don’t know what
this looks like, look online or ask Mrs. Leong).
Pick a complex number, any complex number:
c = a + bi. Plot it on your graph in pencil.
Use this flow chart to find a sequence
of numbers: z0, z1, z2.
That is, take your z0, square it by
FOILing the multiplication of it times
itself, and then add the original c to get
your next number, z1. Now take z1,
square it and add c to get z2.
z0 = c =
z1 =
z2 =
Show your work to get z1 and z2 here. Have Mrs. Leong check your work:
How big is z2? Is it big (numbers bigger than 100)? Is it medium
(numbers from 5 to 100)? Or is it small (small numbers and
fractions/decimals)?
If it is small, color it red, since after many times through the feedback loop
it will probably still be small (it stays in the same area of the graph, close
to zero). If it is big, color it green, since it goes far away from its original
location: every time through the loop it will get bigger and bigger.
II.
Try the following points: compute z1 and z2, showing your FOIL
work! Then color the point red or green, depending if it stays small or
goes off large toward infinity. If the number is medium, leave it
uncolored (in pencil): we might be able to color it in later.
1) c = 5 + 3i
2) c = 2 + 4i
III.
3) c = 1 + 1i
4) c = -0.5 +0.5i
Try each of the following seeds as your c value, using the method
described above. Then plot these points and color them in
appropriately.
0+0i
0+1i
0+2i
0 - 1i
0 - 2i
1+0i
2+0i
-1+0i
0.5+0.5i
-2+0i
0.5 - 0.5i
1+2i
-0.5 - 0.5i
2+1i
0.25+0.25i
2+2i
0.25 - 0.25i
1 - 1i
-0.25+0.25i
-1+1i
-0.25 - 0.25i
-1 - 1i
Come up with 5 more complex numbers of your own choosing and
plot them on your graph, colored appropriately.
IV.
What do you notice about your red points and green points? Find an
online picture of the Mandelbrot Set, print it out to attach to this page
and your graph paper.