C++ RNG (Mersenne Twister) needs seed

I have written a RNG class which holds different algorithms, however it does not work as expected. Besides the fact that i want use normal (rather than uniform) distribution my code always returns either the same number (max) or just 2 numbers out of the interval [min,max]:

std::function<int(int, int)> mt19937 =
    [](int min, int max) -> int {
        std::uniform_int_distribution<int> distribution(min, max);
        std::mt19937 engine;
        engine.seed(time(null));
        auto generator = std::bind(distribution, engine);
        return generator();
    };

Can anyone explain me what is missing to solve this puzzle? Furthermore, how can i implement normal distribution? Last time i tried out std::normal_distribution i was no开发者_开发知识库t able to enter bounds!

EDIT: When i speak of a normal distribution i mean that the results of the RNG near the two bounds should not be generated as often as the mean of both. E.g. look at the graphical representation of the standard Gauss distribution. I am referring to it because it visualizes the probabilities of the resulting values which i want to implement/use this way, if you understand.

The normal distribution is just this (x is a random uniform number):

But I see something that could be problematic:

std::uniform_int_distribution<int> distribution(min, max);

Isn't this giving your number generator an int type?

To fix the seeding problem, create your engine outside of the lambda and seed it when you create it.

A RNG uses an algorithm that produces numbers that appear random, but have a a very large period of repetition (a highlight of the Mersenne Twister). When you seed, you give the RNG an initial value to start the process with. Each time you ask for another number, it spits out another iteration of the algorithm.

When you seed every iteration:

time(NULL)

this code changes only every second, so when you request a new random number, it will only change every second.