random chain

# you can copy/paste the code to here and run it in browser
# http://www.tutorialspoint.com/execute_julia_online.php

# a simple sigmoid shrink function that wraps x to a range between 0 and 1
shrink_fun(x) = 1 / (1 + e^-x)

# a random function generator, 
# it makes a function that maps x to a random point between 0 and 1
function gen_fun()
  n = -1.0 + 2*rand() # a random number between -1 and 1
  function fun(x)
    shrink_fun(n * x)
  end
  fun
end

# a function generator that creates n random functions f1...fn
# and chain them together x->fn(fn-1(...f1(x)))
function gen_chain(n)
  funs = [gen_fun() for i in 1:n]
  function chain(x)
    ret = x
    for i in 1:n
      ret = funs[i](ret)
    end
    ret
  end
  chain
end

# get a chain and run it on some different inputs, what would you expect?
chain1 = gen_chain(100)
println(chain1(rand()*100))
println(chain1(rand()*123))