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Showing content from https://en.cppreference.com/w/cpp/language/../atomic/../algorithm/ranges/generate.html below:

std::ranges::generate - cppreference.com

1) Assigns the result of successive invocations of the function object gen to each element in the range [first, last).

The function-like entities described on this page are algorithm function objects (informally known as niebloids), that is:

Explicit template argument lists cannot be specified when calling any of them.
None of them are visible to argument-dependent lookup.
When any of them are found by normal unqualified lookup as the name to the left of the function-call operator, argument-dependent lookup is inhibited.

[edit] Parameters first, last - the iterator-sentinel pair defining the range of elements to modify r - the range of elements to modify gen - the generator function object [edit] Return value

An output iterator that compares equal to last.

[edit] Complexity

Exactly ranges::distance(first, last) invocations of gen() and assignments.

[edit] Possible implementation

struct generate_fn
{
    template<std::input_or_output_iterator O, std::sentinel_for<O> S,
             std::copy_constructible F>
    requires std::invocable<F&> && std::indirectly_writable<O, std::invoke_result_t<F&>>
    constexpr O operator()(O first, S last, F gen) const
    {
        for (; first != last; *first = std::invoke(gen), ++first)
        {}
        return first;
    }
 
    template<class R, std::copy_constructible F>
    requires std::invocable<F&> && ranges::output_range<R, std::invoke_result_t<F&>>
    constexpr ranges::borrowed_iterator_t<R> operator()(R&& r, F gen) const
    {
        return (*this)(ranges::begin(r), ranges::end(r), std::move(gen));
    }
};
 
inline constexpr generate_fn generate {};

[edit] Example

#include <algorithm>
#include <array>
#include <iostream>
#include <random>
#include <string_view>
 
auto dice()
{
    static std::uniform_int_distribution<int> distr{1, 6};
    static std::random_device device;
    static std::mt19937 engine {device()};
    return distr(engine);
}
 
void iota(auto& r, int init)
{
    std::ranges::generate(r, [init] mutable { return init++; });
}
 
void print(std::string_view comment, const auto& v)
{
    for (std::cout << comment; int i : v)
        std::cout << i << ' ';
    std::cout << '\n';
}
 
int main()
{
    std::array<int, 8> v;
 
    std::ranges::generate(v.begin(), v.end(), dice);
    print("dice: ", v);
    std::ranges::generate(v, dice);
    print("dice: ", v);
 
    iota(v, 1);
    print("iota: ", v);
}

Possible output:

dice: 4 3 1 6 6 4 5 5
dice: 4 2 5 3 6 2 6 2
iota: 1 2 3 4 5 6 7 8

[edit] See also saves the result of N applications of a function
(algorithm function object)[edit] assigns a range of elements a certain value
(algorithm function object)[edit] assigns a value to a number of elements
(algorithm function object)[edit] applies a function to a range of elements
(algorithm function object)[edit] fills a range with random numbers from a uniform random bit generator
(algorithm function object)[edit] assigns the results of successive function calls to every element in a range
(function template) [edit]

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