mandelbrot set

follows on the complex numbers topic going rouge - not related to course concepts, but awe aspiring

sequences !!?

recursive formula for an arithmetic sequence
T1 = 2
Tn+1 = Tn+3
for any number n, find the values in the sequence given by n^2 + n
- some numbers approach infinity e.g. 1 - 1, 1, 2, 5, 26, 677, 458330, 2.11x10^11, 4.41x10^22,1.95x10^45, 3.79x10
- some numbers such as 0.2 give sequences of number which will stay small forever
- -1 oscillates back and forth!
the process we just used can be defined as the following;
- $T_{1} = n$
- $T_{n + 1} = T_{n}^{2} + T_{1}$
which values of $T_{1}$ give a sequence whose $T_{n}$ values stay small forever? (and does not approach infinity)
-2 - 0.25 is the rough range where numbers stay small forever following the sequence!
plot the black numbers (smallest forever) in the complex plane, what shape would you get?