Do you even know if there IS every basic trick?  o.O

K, so when we want to create a 3D environment, we need to have some way to store the world as data.  if we wanted, we could store every coordinate of every triangle that makes up the walls and floor and objects.  BUT, since we want to be as memory efficient as possible, we will store the world as a simple matrix.  The world well be made up of a series of blocks that lay on a grid.  A 1 in the matrix might represent a block, and a zero might represent an empty space:

[1,1,1,1,1,1,1,1]
[1,0,0,0,0,0,0,1]
[1,0,0,0,0,0,0,1]
[1,1,1,1,1,1,1,1]
 
Now, in order to render the image on screen, we need to consider how it will look.  There are 96 pixels from left to right, and that is 96 times we need to decide what kind of column to draw (remember, every pixel in a single column is responding to the same distance, so we don't have to go pixel by pixel, only column by column)

If we consider a view of a wall, we can see the farther it gets away, the smaller it gets.  The actual formula is aparentHeight = Arctan(ActualHeight/Distance) , but this is almost exactly equal to aparentHeight = ActualHeight/Distance, and this way is faster.

So in each column of pixels, we will draw a single slice of wall that is a certain distance away.  We have the formula, now all we need is the distance.  This is where the raycasting comes in.

We are at a certain position, and we are facing a certain direction.  In order to find the distance in front of us until we hit a wall, we just need to move us forward until we hit a wall.  You can then do this many more times at many slightly different angles to get all the distances you need (96).

It is then a simple matter to use your information and the formulas to create an amazing, texterless wall!  Textures are MUCH harder, and will be the subject of another lesson if you are still confused.

Hope that helped!  I made a raycasting game in java a while back, so I know a thing or too 

Welcome welcome Welcome!
I'm kinda new here too, but I can still say WELCOME!

I love that site

Well... I suppose, but it seems a bit excessive for a replacement of a simple recall 

Thanks!  I liked the xLib version too, I just felt it needed to be revamped with more puzzles and faster speed.

You could put all those under a separate category, so each would be competing against programs of the same type

"comes back"
Hmmm, it works alright now, and I don't think I did anything differently.
Oh well, if it works, I'm happy.