Mathematica Help

[RyanJ]

Hey guys!

 

It has been a while since I posted so hopefully this one will be good.

 

Basically I have a table of prime numbers. What is to write this table as an image - from 1 too 480000 - showing each cell that is a prime as white and the others as black.

 

So basically I'm cycling the numbers from 1-480000 and if they are prime then I want the cell white and otherwise black. I also want to be able to wrap the table to 800x600 pixels.

 

Any help appreciated.

[JohnB]

I wonder what the picture will look like?

[Cap'n Refsmmat]

This looks like what you want:

 

http://reference.wolfram.com/mathematica/tutorial/ImageProcessing.html

 

You can use Table[] to make the matrix of values:

 

http://reference.wolfram.com/mathematica/ref/Table.html

 

Not sure how exactly that'd work, but you can probably work out a way that'll work...

[RyanJ]

The closest I've got so far is this:

 

Image[Table[if[PrimeQ[x], 1, 0], {x, 1, 800}, {y, 1, 800}]]

 

That makes an image but shows each line as either black or white instead of each cell.

 

I know I need to build a table and put it into the Image function but I can't figure out how to do it.

[the tree]

You want to enumerate the cells in a sensible way, try

PrimeQ[ x+800*(y-1)]

[Cap'n Refsmmat]

The closest I've got so far is this:

 

Image[Table[if[PrimeQ[x], 1, 0], {x, 1, 800}, {y, 1, 800}]]

 

That makes an image but shows each line as either black or white instead of each cell.

 

I know I need to build a table and put it into the Image function but I can't figure out how to do it.

 

That's because you're only testing the row number, not the cell. I'd do:

 

Image[Table[if[PrimeQ[x*800 + y], 1, 0], {x, 0, 799}, {y, 0, 799}]]

 

I think that gives the right result.

 

edit: err, wait, that might go vertically instead of horizontally. But you get the idea.

[RyanJ]

This is the formulation I ended up working with. It does what I need:

 

Size = 300
Image[Table[if[PrimeQ[y* (Size - 1) + x], 1, 0], {x, 1, Size}, {y, 1, Size}]]

 

Edit: That actually doesn't seem to work correctly. I may need to do some more work on it.

Edited April 15, 2010 by RyanJ

[RyanJ]

II eventually gave up on trying to perfect the formula in Mathematica so I wrote a program to generate the code for me. Here is the resulting image if anyone is interested:

 

http://bayimg.com/lAlKLaaCp

 

The highest prime used in this list is 104729.

[JohnB]

Fascinating.

 

The horizontal hold on your Prime numbers needs adjusting.

[RyanJ]

I think that is just the rest of the number I chose to fold the lines. When I choose 10 cells per line it doesn't have the horizontal rows like that.

[JohnB]

Ryan, I was thinking of the diagonal lines. Presumably, depending ton the grid size you choose, you could get a number of different patterns emerging.

 

Either way. I was quite pleased to see the result.

 

Nicely done.

[RyanJ]

Yeah. I understand what you are saying.

 

I can upload the C# project if anyone else wants to experiment with it. To see what other things we can do.

 

Though you would need Mathematica in order to process the codes.