Einstein

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

I like the experiment!
In this 128x128 magic square the lowest numbers 1-1024 are in the centre.
This numbers are coded in grayscale.
Number 1 is white and number 1014 is black. The other numbers are ordered in between, so slowly it goes from white to black. How bigger the number the more black.

And this is the result

A very special Magic Square

A magic square with in de centre the lowest numbers 1 -256.

The numbers are organised so that 1-4 are in the centre. 

Around there is a layer from the numbers 5 -16.

In the next layer around the numbers 17-36

And so on:

37-64

65-100

etc and the last (outside) layer 193-256

The square is magic because the sum of the numbers in each row, column and all diagonals are the same: 131104

The extra in this square is that in this centre the 2 by 2 squares are connected
The sum of the middle 2x2 square: 10
1+2+3+4
The sum 2x2 squares of the layer around is 34
16+7+10+1 and 8+15+2+9 and 12+3+14+5 and 4+11+6+13
The sum of de 2x2 squares in the layer around is 82
25+18+23+16 and33+34+7+8 and 17+26+15+24 and 9+30+11+32 etc
in the next layers the sum of the 2x2 squares are:
162 - 274 - 418 - 594 and 802

The centre with the layers

and the total 64x64 square