"Foldable Array" puzzle live: http://jsbin.com/ibewis/6/edit

FoldableArrayStructureDemo.js

/* 
example: 

// [1,2,3,4,5,6,7,8] (must be a power of 2 length)

var arr = new Foldable([1, 2, 3, 4, 5, 6, 7, 8]);

arr.fold( [ "l", "r", "l" ] ); // left, right, left

// left

  [4, 3, 2, 1]
  [5, 6, 7, 8]

//right

  [8, 7]
  [1, 2]
  [4, 3]
  [5, 6]


//left and final result

  [5]
  [4]
  [1]
  [8]
  [7]
  [2]
  [3]
  [6]

*/

(function () {

    'use strict';

    var pow2exp = function (n) {
       return Math.log(n) / Math.log(2); 
    };
  
    var Foldable = function (arr) {
        if ( !arr || !arr.length || ( ( pow2exp( arr.length ) % 1 ) !== 0 ) ) {
            throw new Error("Initial array must be of a power of 2 length");
        }
        this._arr = arr;
        this._2d = [arr];
    };

    Foldable.prototype = {
        fold: function (steps) {
            var len = this._foldLength();

            if (!steps || !steps.length) return;

            for (var i = 0; i < len; i++) {

                if (steps[i] === 'r')
                    this._foldRight();
                else if (steps[i] === 'l')
                    this._foldLeft();
            }
        },

        get2DResult: function () {
            return this._2d;
        },

        getFlatArray: function () {
            var _arr = [];
            this._2d.forEach(function (a) {
                _arr.push(a);
            });
            return _arr;
        },

        toString: function () {
            var str = "[\n";
            this._2d.forEach(function (arr) {
                str += "\t[" + arr + "]\n";
            });
            str += "]\n";
            return str;
        },

        _foldLeft: function () {
            var _new_2d = [];
            for (var i = 0; i < this._2d.length; i++) {
                var left = this._2d[i].slice(0, this._2d[i].length / 2);
                var right = this._2d[i].slice(this._2d[i].length / 2, this._2d[i].length);
                left.reverse();
                _new_2d.unshift(left);
                _new_2d.push(right);
            }
            this._2d = _new_2d;
        },

        _foldRight: function () {
            var _new_2d = [];
            for (var i = 0; i < this._2d.length; i++) {
                var left = this._2d[i].slice(0, this._2d[i].length / 2);
                var right = this._2d[i].slice(this._2d[i].length / 2, this._2d[i].length);
                right.reverse();
                _new_2d.unshift(right);
                _new_2d.push(left);
            }
            this._2d = _new_2d;

        },

        _foldLength: function () {
            return pow2exp(this._arr.length);
        }

    };

    // test
    var farr = window.a = new Foldable([1, 2, 3, 4, 5, 6, 7, 8]);
    console.log(farr.toString());
    farr.fold(["l", "r", "l"]);
    console.log(farr.toString());
})();