Array Difficulties

I have a Radio Shack RGB Tri-Color LED strip. I am trying to set it to scroll through colors as I turn a potentiometer knob.
This is currently how it is programmed... There's got to be a better way. I would like to have every combination corresponding to a color, which, I assume, need to be mapped to the potentiometer?

PROGMEM const unsigned long color_1[1][10]={
{0xf00000,0xf00000,0xf00000,0xf00000,0xf00000,0xf00000,0xf00000,0xf00000,0xf00000,0xf00000}
};

PROGMEM const unsigned long color_2[1][10]={
{0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000,0x0f0000}
};

PROGMEM const unsigned long color_3[1][10]={
{0x00f000,0x00f000,0x00f000,0x00f000,0x00f000,0x00f000,0x00f000,0x00f000,0x00f000,0x00f000}
};

PROGMEM const unsigned long color_4[1][10]={
{0x000f00,0x000f00,0x000f00,0x000f00,0x000f00,0x000f00,0x000f00,0x000f00,0x000f00,0x000f00}
};
.
.
.
.
etc...

I don’t understand the point of a 1x10 array, and I’m not even sure I understand why you’re using an array.
If all you want to do is move a four bit mask around, then the << and >> shift operators seem to fit the bill.

You send the same color 10 times?
Doesn't that suggest something?

There are 10 different segments of LEDs that can all be different colors, so I'd think each LED segment world require a color right?

But if all you're doing is this:
0xf0000000
0x0f000000
0x00f00000
0x000f0000
etc,
why do you need arrays?

Marinonix:
There are 10 different segments of LEDs that can all be different colors, so I'd think each LED segment world require a color right?

For sure, but if the 10 values for each set are the same, you should only need to store one value for each set which you can just repeat.

AWOL pointed out you could simply shift 0xF00000 right ( 4 * x ) bits where x is the index of the segment. There is no real need for an array.

What is your motivation for a first dimension of 1? It is the same as not having the extra dimension at all.

Also the repeating variable names requires repeated code to use, arrays are extremely useful for this situation ( 1 array with an extra dimension ):

const unsigned long color_1[10];
const unsigned long color_2[10];
const unsigned long color_3[10];
//...
//Or

const unsigned long color[ 3 ][ 10 ];

You send the color bytes to the strip. If there are 10 the same then send the same bytes 10 times.
Change the bytes to the next color, wash, rinse, repeat.

And maybe do the examples in section 5 of your IDE Examples to get a choice of tools to work with.
IDE File menu, click Examples and up near the top of the popup menu click on 5.Control.
Learn these to start learning the fundamental program control structures, and using arrays.
Do the simple things before trying harder things.