Do crystal lattices always make an exact pattern? Years ago I read something that said in crystals "atoms have finite positions along the crystal lattice."
What I took that to mean was that in any crystal structure, atoms have a finite number of possible positions. Which is what I want to find out here.
After searching images for crystalline structures I found that all of them represent atoms as tiny balls that line up perfectly in a regular pattern.

What I take all this to mean is that, in a crystal structure, atoms can only exist in very specific places in accordance with their patterns like a cube made out of Lego bricks. They can only exist in, for want of a better word, a digital fashion. They always form straight edges and if another atom is added, it's like another Lego brick has been added to the cube, it can only be fitted in exactly according to its grid like structure. The atom can only be in column one row six or column three row four and so on. Like pixels on the screen.

My understanding is that, in a crystal lattice, atoms cannot take positions in an analogue way, they cannot be positioned in a lattice a few micro metres one way or the other.
What I conclude from this reasoning is that there is only a finite number of shapes that any crystalline material can take because of the digital nature of the positioning of the atoms, as opposed to the analogue way you can sculpt plasticine.
Is this so?
If we could shrink down to the atomic level and look at a crystalline solid with the entire structure look like a Lego sculpture or a pixelated image? Or do the atomic patterns allow for some degree of analogue placement?
I have read there is such a thing as screw dislocations.

Does this say that although crystal atoms do generally have a pattern, that pattern is not rigid and inflexible?
When you pour liquid glass into a spherical mould and let it cool or sculpt something out of clay and fire it, do the crystal lattices that form bend to accommodate these curved edges? Or is the solid still cubic in pattern and it just seems to be analogue because it's too small to be seen? Do screw defects only occur when someone or something is applied pressure to the crystal or do they naturally form with curved lattices?
And yes I'm aware crystal grains have non-latticed atoms between them and sometimes there is a missing atom in the lattice. But that's not what I'm talking about here.
To put it as simply as I can, to crystals onlay ever exist as lego scuptures or can the grow like trees with curved bows?
Edit: when I say crystals I mean crystals like what we call in every day life like pyrite and quartz, materials like stone and ceramics.
Thank you for your attention.
 A: 
Does this say that although crystal atoms do generally have a pattern, that pattern is not rigid and inflexible?

This line is the essence of your question. And the answer is: yes, some flexibility is possible.
In the crystal-structure models you show, each atom is tied to its position in the lattice via chemical bonds of various sorts and strengths. These bonds are to some degree flexible. 
Also, the size of the atom is not well-defined. We like to draw it as a spherical ball for convenience, but it is rather a "cloud"-like thing with no clear edge due to the orbiting electrons' wave forms. These shapes are also slightly flexible and atoms can be squeezed slightly.
So, there are several means of flexibility.


*

*Lattices may look rigid and fully straight locally over short distances (across not-too-many atoms) - just like you don't see the glass pole, the steel beam or the Lego building bend over a few centimetres.

*But look across a very large lattice, and it may have been bent, twisted or in other ways displaced from its ideal, rigid structure - just like a long glass pole, steel beam or large Lego building visibly bend over several metres without breaking.


Just think of the fact that atoms have different effective sizes. Combining different atoms in a lattice or inserting a substitution atom of a different type into an until-then well-defined lattice will have to distort the lattice and twist and turn chemical bonds simply in order to make the lattice hold itself together. Distortion and flexibility has to be possible.
So, your first-shown illustration with atoms as balls in a perfectly ideal lattice is an example of the first situation; a structure seen over a short distance. Your other illustrations with models showing lattice dislocations are examples of the other situation; the larger atomic structure, so large that you can't see individual atoms at this scale, which can be significantly misaligned over a relatively longer distance.

Note, regarding your wording, you mention screw dislocations, but be aware that the screw is only one among several different types of dislocations (as you illustrations also show).
