[01, 02, 03, 04]
[05, 06, 07, 08]
[09, 10, 11, 12]
[13, 14, 15, 16]

#1        |   #2
[01, 02]  |  [03, 04]
[05, 06]  |  [07, 08]
----------+-----------
#3        |   #4
[09, 10]  |  [11, 12]
[13, 14]  |  [15, 16]

#1       

[01, 03]
[09, 11]

#1       

[01, 04]
[13, 16]

var arr = [[1,2,3,4],
           [5,6,7,8],
           [9,10,11,12],
           [13,14,15,16]
           ],
    step = 1;
for(i=0; i < 4; i=i+step*2) {
	for(j=0; j < 4; j=j+step*2) {
    	var dot1 = arr[i][j],
            dot2 = arr[i][j+step],
            dot3 = arr[i+step][j],
            dot4 = arr[i+step][j+step];
        alert("Section" + (i+j) + ": [" + dot1 + ", " + dot2 + ", " + dot3 + ", " + dot4 + "]");
	}
}

[
 [1,4]
 [13,16]
]

function matrix(c, d) {
    for (var g = [], a = 0; a < d * d; a += c) {
        for (var f = [], e = [], b = 0; b < c; b++) e.push(a + b + 1);
        f.push(e);
        for (b = 0; b < c - 1; b++) e = e.map(function(a) {
            return a + d
        }), f.push(e);
        g.push(f);
        !a || (a + c) % d || (a += d * (c - 1))
    }
    return g
};
alert(JSON.stringify(matrix(2,4)))// матрицу 4 на 4 разбить 2 на 2
alert(JSON.stringify(matrix(3,9)))//этоn же вариант и для матрицы 9 на 9 на 3 на 3 ... matrix(3,9)

var a = [
    ['01', '02', '03', '04'],
    ['05', '06', '07', '08'],
    ['09', '10', '11', '12'],
    ['13', '14', '15', '16']
], b = [], i, s = 2;

for(i=0; i<a.length/2; i++) {
    b.push(a[i].slice(0, s), a[i+1].slice(0, s));
    b.push(a[i].slice(s), a[i+1].slice(s))
}

console.log(b)

b.push([a[i].slice(0, s), a[i+1].slice(0, s)], [a[i].slice(s), a[i+1].slice(s)])
//[[["01", "02"], ["05", "06"]], [["03", "04"], ["07", "08"]], [["05", "06"], ["09", "10"]], [["07", "08"], ["11", "12"]]] в консоли, или не то?

function split(src, dist, step, row, column) {
    if (row + step < src.length) {
        dist.push([
            [src[row][column], src[row][column + step]],
            [src[row + step][column], src[row + step][column + step]],
        ]);
        if (column + step + 1 < src[0].length) {
            return split(src, dist, step, row, column + step + 1);
        } else {
            return split(src, dist, step, row + step + 1, 0);
        }
    }
    return dist;
}

var arr = [
    [1,2,3,4],
    [5,6,7,8],
    [9,10,11,12],
    [13,14,15,16]
];

console.log(split(arr, [], 1, 0, 0));
console.log(split(arr, [], 3, 0, 0));

var arr = [
[1,2,3,4,5,6,7,8,9],
[10,11,12,13,14,15,16,17,18],
[19,20,21,22,23,24,25,26,27],
[28,29,30,31,32,33,34,35,36],
[37,38,39,40,41,42,43,44,45],
[46,47,48,49,50,51,52,53,54],
[55,56,57,58,59,60,61,62,63],
[64,65,66,67,68,69,70,71,72 ],
[73,74,75,76,77,78,79,80,81]
];

var arr=[[[1, 2, 3], [10, 11, 12], [19, 20, 21]], [[4, 5, 6], [13, 14, 15], [22, 23, 24]], [[7, 8, 9], [16, 17, 18], [25, 26, 27]], [[28, 29, 30], [37, 38, 39], [46, 47, 48]], [[31, 32, 33], [40, 41, 42], [49, 50, 51]], [[34, 35, 36], [43, 44, 45], [52, 53, 54]], [[55, 56, 57], [64, 65, 66], [73, 74, 75]], [[58, 59, 60], [67, 68, 69], [76, 77, 78]], [[61, 62, 63], [70, 71, 72], [79, 80, 81]]]

var a = [
    ['01', '02', '03', '04'],
    ['05', '06', '07', '08'],
    ['09', '10', '11', '12'],
    ['13', '14', '15', '16']
], b = [], i, s = 2;

for(i = 0; i<a.length; i += s) {
    b.push([a[i].slice(0, s), a[i+1].slice(0, s)], [a[i].slice(s), a[i+1].slice(s)])
}

console.log(b)

function matrix(c, d) {
    for (var h = [], a = 0; a < d * d; a += d * (c - 1))
        for (var f = 0; f < d; f += c) {
            for (var g = [], e = [], b = 0; b < c; b++) e.push(a + b + 1);
            g.push(e);
            for (b = 0; b < c - 1; b++) e = e.map(function(a) {
                return a + d
            }), g.push(e);
            h.push(g);
            a += c
        }
    return h
};
alert(JSON.stringify(matrix(2,4)))
alert(JSON.stringify(matrix(3,9)))
console.log(matrix(3,9))

function split(src, st, r, c) {
    if(!st) return false;
    if (r + st < src.length && c + st < src[0].length) { 
    console.log(st +"---------"+src[r][c]+","+ src[r][c + st]+","+src[r + st][c]+","+ src[r + st][c + st]);
	if (c + st +1 < src[0].length) {
            return split(src, st, r, ++c + st);
        } else {
            return split(src, st, ++r + st, 0);
        }
    } else split(src, st==1?0:Math.ceil(st/2), 0, 0);
}

var arr = [
    [1,2,3,4],
    [5,6,7,8],
    [9,10,11,12],
    [13,14,15,16]
];
split(arr, 3, 0, 0);

var a = [
    ['01', '02', '03', '04'],
    ['05', '06', '07', '08'],
    ['09', '10', '11', '12'],
    ['13', '14', '15', '16']
], b = [], i, s = [B]2[/B];

for(i = 0; i<a.length; i += s) {
    b.push([a[i].slice(0, s), a[i+1].slice(0, s)], [a[i].slice(s), a[i+1].slice(s)])
}

console.log(b)

var arr = [],
    step = 5, // offset between choosen positions
    size = 11; // grid size ~ 11x11

for(i = 0; i < size; i++) { // fill array
  arr.push([]);
  var str = '';
  for(j = 0; j < size; j++) {
    arr[i][j] = i * size + j;
    str+=addZero(''+arr[i][j], 3)+', ';
  }
  console.log(str); // draw array
}

for( i = 0 ; i + size * step < arr.length * size; i+=step) { // use ' i+=step' to start from last X pos (ex. 0-1, 1-2), else use ' i+=step+1' to reduce repetition (ex. 0-1, 2-3)
  var row = Math.floor(i / size), 
      column = Math.floor(i % size);
  
      if( row == Math.floor((i + step) / size)  && row % step == 0) { 
    
      console.log(
        '-----'+
        arr[row][column]+","+ 
        arr[row][column + step]+","+
        arr[row + step][column]+","+ 
        arr[row + step][column + step]
      );
      }
  }

function addZero(str,length) { // add 0 to fill str length
  while(str.length < length) {
    str = '0'+str;
  }
  return str;
}