Questions tagged [lattices]
The lattices tag has no usage guidance.
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Can a LatticeData image be displayed in a space filled fashion
I'd like a FaceCenteredCubic image as in the in LatticeData
docs, but space packed, and cropped on all the boundaries, so that it illustrates the geometry of the calculation that leads to the $\pi/\...
23
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4
answers
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How to create an hexagonal lattice structure
Given an array of atoms A-B-A-B-A-B in an hexagonal pattern, how can I use Mathematica to create with an hexagonal lattice (infinite) with this array so each atom A is sorrounded only by B atoms and ...
11
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3
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Creating a Hexagonal Lattice with VoronoiMesh
I want to create a hexagonal lattice using VoronoiMesh. One can achieve that with the following code, where L=5,
...
8
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4
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Drawing a trihexagonal tiling
I am trying to draw a trihexagonal tiling of the following form
using Mathematica. I attempted to begin by using the result given in this Stack Overflow Q & A. However, I couldn't figure out how ...
9
votes
1
answer
465
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Generating a Periodic Voronoi Mesh
Consider the following hexagonal mesh, created from VoronoiMesh
...
1
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1
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800
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Using LatticeData to fill a space with spheres in a face-centered cubic (fcc) lattice packing arrangement
I have a large sphere of radius $R_1$ which I would like to pack with $N$ smaller radius of radius $r_2<R_1$ arranged in a face-centered cubic (fcc) packing arrangement (i.e. Kepler's optimal ...
0
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1
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642
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Mathematica Lattice Reduce Command
I'm going through a very old copy of "Mathematica: A System for Doing Mathematics by Computer" for self practice.
I'm on chapter 3, and ran into the LatticeReduce ...
12
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3
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503
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How to generate grid points on boundary of $[-1,1]^d$ for arbitrary dimension $d$ and specified resolution?
This must be a trivial thing, but I was not able to find a function for it in Mathematica. How do you efficiently create a grid with constant but specific resolution $r$ in all directions on the ...
6
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How to generate a 3-d simple cubic lattice of length 4 in each dimension?
LatticeData["SimpleCubic", "Image"]
The above line gives me a single cube (2 lattice points in each direction).
But I want a lattice with 4 lattice points in ...
2
votes
2
answers
297
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Defining a piecewise function with underlying lattice
I'm fairly new to Mathematica, and programming in general, but I'm trying to define an $n$-dimensional piecewise function, $F({\bf x})$. Properties of the function are set by an underlying lattice, ...
21
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2
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How to build a neighbor table for the Hexagonal lattice
I want to consider a collection of vertices arranged in a finite Hexagonal lattice, with say $n_{r}$ rows and $n_{x}$ vertices per row, for a total of $N = n_{x}n_{r}$ vertices. The goal is to ...
14
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3
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Ordering Problem With VoronoiMesh
Imagine I want to model 2D cells moving in a tissue. Consider, as an example, Lloyd's relaxation algorithm. Using VoronoiMesh I'm able to mimic some cell movement. ...
12
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2
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Arbitrary lattice graph in 2D
My purpose is to generate a graph representing a lattice, where the vertices are essentially the lattice sites. This lattice has to be periodic. That means the opposite boundaries are identical.
MWE ...
8
votes
1
answer
497
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How can I sequentially apply different graph embeddings?
Imagine I have some graph G, and I perform a graph embedding using a command like:
...
7
votes
1
answer
326
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construct a lattice with a defined unitcell
We can construct a base-centered tetragonal unit cell by:
LatticeData["CenteredTetragonal", "Image"]
But how can we construct a lattice by <...
7
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3
answers
402
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Creating MeshRegions of various 2D lattices
This is a soft question about the best approach to design a function that creates MeshRegion objects of various 2D lattices, e.g. kagome or hexagonal, all through ...
6
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3
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875
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Drawing a Kagome lattice for given geometry
I came across this question in stack exchange. Modified the answer a bit to get a lattice structure like this.
...
6
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2
answers
245
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Automatically get points in a given triangular lattice and vice versa?
Given a triangular lattice which grows with number n, as follows
I want to list all the connected points in the lattice to form the ...
4
votes
1
answer
840
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Hexagonal lattice points with center points in 2D
I am using the follwing coder from here, answered by Michael E2, to create 2d lattice points, without the center ponts of the cells.
...
4
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2
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655
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Minimise discrete function
Let $f\,\colon\,\Lambda\to\mathbb R$ be a real-valued function, where $\Lambda$ is a finite integer lattice. Say, $\Lambda=\mathbb Z_3^n=\{\vec x\,\mid\, x_i=0,1,2\}$ for some $n\in\mathbb N$. I'd ...
4
votes
3
answers
255
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Cell-adjacency Graph of a Square Mesh
Consider the list of points
pts = {{1, 1}, {1, 2}, {2, 1}, {2, 2}}
I want to use them to define a 2x2 square mesh using ...
2
votes
1
answer
611
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Cropping a non-cubic lattice unit cell
I would like to crop the hexagonal close-packed system as a hexagon and not as a cube. I would like to use the following volumetricPlot already given on this ...
2
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1
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Finding 111 plane of Carbon Diamond
All,
I looked at the example on the Mathematica Website with the Carbon Diamond Lattice.
Example I am referring to
I am wondering is there a way to highlight an individual plane such as the 111 or ...
1
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1
answer
337
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Point lattice leading to triangle lattice
My main purpose is to eventually generate a triangle lattice from one original point, let's say the origin. So I want to start with the origin and generate 6 points around it, which are the vertices ...