Q:

Malloc a 3-Dimensional array in C? 

I'm translating some MATLAB code into C and the script I'm converting makes heavy use of 3D arrays with 10*100*300 complex entries.  The size of the array also depends on the sensor's input, ideally the array should be allocated dynamically.   So far I've tried two approaches the first being a flat 1D array along the lines of
value = array[x + (y*xSize) + (z*ySize*xSize)]

Which hurts my brain to use.  I've also tried an array of an array of pointers
int main () {
  int ***array = malloc(3*sizeof(int**));
  int i, j;

  for (i = 0; i < 3; i++) {
    *array[i] = malloc(3*sizeof(int*));
    for (j = 0; j < 3; j++) {
      array[i][j] = malloc(3*sizeof(int));
    }
  }

  array[1][2][1] = 10;

  return 0;
}

Which gives a seg fault when I try to assign data. 
In a perfect world, I'd like to use the second method with the array notation for cleaner, easier programming.  Is there a better way to dynamically allocate a three-dimensional array in C? 

A:

I'd go for the first option (the single 1D array) as it will give you a single block of memory to play in rather than potentially thousands of fragmented memory blocks
If accessing the correct element of the array is doing your head in though, I'd write a utility method to convert x, y, z locations into an offset into the 1D array
int offset(int x, int y, int z) { 
    return (z * xSize * ySize) + (y * xSize) + x; 
}

A:

As others have said, it is probably better to allocate one contiguous chunk of memory, and then figure out the indexing yourself.   You can write a function to do so if you want.   But since you seem to be interested in knowing how to deal with the multiple malloc() case, here is an example:
First, I define a function free_data(), which frees an int *** with xlen and ylen as the first two dimension sizes.   We don't need a zlen parameter just like free() doesn't take the length of the pointer being freed. 
void free_data(int ***data, size_t xlen, size_t ylen)
{
    size_t i, j;

    for (i=0; i < xlen; ++i) {
        if (data[i] ! = NULL) {
            for (j=0; j < ylen; ++j)
                free(data[i][j]);
            free(data[i]);
        }
    }
    free(data);
}

The function loops over the pointer data, finds out the ith int ** pointer data[i].   Then, for a given int ** pointer, it loops over it, finding out the jth int * in data[i][j], and frees it.   It also needs to free data[i] once it has freed all data[i][j], and finally, it needs to free data itself. 
Now to the allocation function.   The function is a bit complicated by error checking.   In particular, since there are 1 + xlen + xlen*ylen malloc calls, we have to be able to handle a failure in any of those calls, and free all the memory we allocated so far.   To make things easier, we rely on the fact that free(NULL) is no-op, so we set all the pointers at a given level equal to NULL before we try to allocate them, so that if an error happens, we can free all of the pointers. 
Other than that, the function is simple enough.   We first allocate space for xlen int ** values, then for each of those xlen pointers, we allocate space for ylen int * values, and then for each of those xlen*ylen pointers, we allocate space for zlen int values, giving us a total space for xlen*ylen*zlen int values:
int ***alloc_data(size_t xlen, size_t ylen, size_t zlen)
{
    int ***p;
    size_t i, j;

    if ((p = malloc(xlen * sizeof *p)) == NULL) {
        perror("malloc 1");
        return NULL;
    }

    for (i=0; i < xlen; ++i)
        p[i] = NULL;

    for (i=0; i < xlen; ++i)
        if ((p[i] = malloc(ylen * sizeof *p[i])) == NULL) {
            perror("malloc 2");
            free_data(p, xlen, ylen);
            return NULL;
        }

    for (i=0; i < xlen; ++i)
        for (j=0; j < ylen; ++j)
            p[i][j] = NULL;

    for (i=0; i < xlen; ++i)
        for (j=0; j < ylen; ++j)
            if ((p[i][j] = malloc(zlen * sizeof *p[i][j])) == NULL) {
                perror("malloc 3");
                free_data(p, xlen, ylen);
                return NULL;
            }

    return p;
}

Note that I have simplified malloc calls quite a bit:  in general, you shouldn't cast the return value of malloc, and specify the object you're allocating for as the operand to sizeof operator instead of its type.   That makes malloc calls simpler to write and less error-prone.   You need to include stdlib.h for malloc. 
Here is a test program using the above two functions:
#include <stdlib.h>
#include <errno.h>
#include <stdio.h>
#include <time.h>

int main(void)
{
    int ***data;
    size_t xlen = 10;
    size_t ylen = 100;
    size_t zlen = 300;
    size_t i, j, k;

    srand((unsigned int)time(NULL));
    if ((data = alloc_data(xlen, ylen, zlen)) == NULL)
        return EXIT_FAILURE;

    for (i=0; i < xlen; ++i)
        for (j=0; j < ylen; ++j)
            for (k=0; k < zlen; ++k)
                data[i][j][k] = rand();

    printf("%d\n", data[1][2][1]);
    free_data(data, xlen, ylen);
    return EXIT_SUCCESS;
}

By all means use this approach if you find it easier to use it.   In general, this will be slower than using a contiguous chunk of memory, but if you find that the speed is OK with the above scheme, and if it makes your life easier, you can keep using it.   Even if you don't use it, it is nice to know how to make such a scheme work. 

A:

Are you sure you need to use malloc?  C allows creating of multidimentional arrays natively:
int a2[57][13][7];

Or you can use malloc in the following way:
int (*a)[13][7]; // imitates 3d array with unset 3rd dimension
                 // actually it is a pointer to 2d arrays

a = malloc(57 * sizeof *a);    // allocates 57 rows

a[35][7][3] = 12; // accessing element is conventional

free(a); // freeing memory

