Sqrt(sqrt(sqrt(...x)

Iterating the square root of a number.
Use a calculator. This is the graph of iterating the square root of 10.
A program in Basic, to get 19 iterations,
would be:

• 10 INPUT N
• 20 For c = 1 to 20
• 30 N = Sqrt(N)
• 40 PRINT N
• 50 Next c

We get an infinite sequence that approaches 1. Try other numbers. Try negative numbers. Try complex numbers. What happens?