A rose made of galaxies

This is the source of the first background image in this blog.

A rose made of galaxies
Credit:
NASA, ESA and the Hubble Heritage Team (STScI/AURA)

Dark matter ring in galaxy cluster

This is the source of the first background image in 4x4.

Dark matter ring in galaxy cluster Cl 0024+17 (ZwCl 0024+1652)
Credit:
NASA, ESA, M.J. Jee and H. Ford (Johns Hopkins University)

What is 4x4?

Those kind of squares made with numbers are called "Magic Square". Among those squares, the 4x4 kind has many interesting properties, such as:

1. Built with 1 to 16 without repeat.
2. The sum of numbers in any row is 34, e.g. 1 + 8 + 10 + 15 = 34.
3. The sum of numbers in any column is 34, e.g. 1 + 12 + 7 + 14 = 34.
4. The sum of numbers in both diagonal is 34, e.g. 1 + 13 + 16 + 4 = 34.
5. The sum of numbers in any sub 2x2 squares is 34 (even cross the edge), e.g. 1 + 8 + 12 + 13 = 34, 12 + 7 + 6 + 9 = 34.
6. The sum of numbers in 4 corners is 34, e.g. 1 + 15 + 14 + 4 = 34.
7. The sum of each corner with their relative 3 numbers is 34, e.g. 1 + 6 + 16 + 11 = 34.
8. In every sub 3x3 squares, the sum of diagonal 2 numbers is 17, e.g. 1 + 16 = 17, 13 + 4 = 17.

Wolfram Mathworld said there are 48 squares comply those rules. But you can shuffle the square:

All columns shift left/right make a new square:

All rows shift up/down make a new one, too.

Switch red and green square at the same time make a new one!

Shuffle with those 3 rules would generate all 48 squares mentioned in Wolfram Mathworld`s page. The 4x4 app for iOS is developed based on these concept. It will be my pleasure if you like this "Magic", too.