# Questions tagged [packing]

Questions about specific or optimal placement of objects in a shape or volume. For questions about packed arrays, use the [packed-arrays] tag.

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### Filling the space with rectangles

Following up on my previous question, I now seek to fill a matrix $m \times n$ with rectangles. Henrik Schumaker had provided some code in his answer to the previous question: ...
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### Rectangle packing, fixed sizes

I have rectangles of a given size to fit into a larger rectangle of a fixed size, with a specified gap between the packed rectangles. I would like to write some code that optimises the number of ...
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### Dense packing of disks with different radii

Let's consider a disk ($D_{1}$) whose center position is randomly generated, but the radius is fixed at $r_{1}$. A second disk ($D_{2}$) of fixed radius $r_{2}$ (with $r_{2} < r_{1}$) is randomly ...
199 views

### Furthest point from nearby objects, packing a sphere on a region interior

Suppose I have a boundary $\partial\Omega$ of a region $\Omega\subset \mathbb{R}^3$ and within this are some compact objects $B_i\subset\Omega$. They could be points, lines, polygons, complex 3D ...
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1 vote
134 views

### Octahedra+tetrahedra filling tessellations in 3D

This is called the quasiregular space-filling tessellations in 3D: formed by Octahedra in RED and tetrahedra in YELLOW Are there any smart ways to do a Mathematica figure drawing this?
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1 vote
251 views

### Draw a truncated octahedron packing in 3D

Consider a truncated octahedron composed by 24 vertices (4×6) 14 faces (contain 6 squares and 8 hexagons) 36 edges (4×6+6×82=36). This truncated octahedron can pack and tessellate the 3-dimensional-...
• 823
349 views

### Embedding non-orthogonal vectors in a vector space

Consider unit vectors $|v_i \rangle$ on an $n$ dimensional vector space, which obey the following relation: \langle v_i|v_i \rangle =1 \quad \& \quad |\langle v_i|v_j \rangle| \leq \epsilon, \...
230 views

### Adjacency Matrix to Clusters of Equal Sizes

I have a system with 72 nodes. I have a binary adjacency matrix $S$ of size $72\times 72$. If $S_{i,j}=1$, then node $i$ is adjacent to node $j$. So, we also have $S_{i,j}=S{j,i}$. So, $S$ is a ...
120 views

### Sphere packing with target volume fraction

I've stumbled upon this sphere packing question, and now I have another related one. How can I have a function that returns a sphere packing with a target volume fraction? Sphere can obviously have ...
• 503
1 vote
115 views

### Reap unpacks packed arrays

I noticed that Reap unpacks packed arrays. I've looked at previous answers but am still an unsure whether this a serious issue. E.g. consider Ex 47.3 from EIWL: ...
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### Generating Doyle spiral painting

I recently came across an interesting paining by Nicola Sutcliffe: This painting is actually related to Doyle spirals. From author's website: The central part of the picture shows the Doyle ...
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462 views

### Wolfram alpha algorithm for geometric packing in 2D [closed]

Is there any way to gain access to the algorithm that wolfram alpha uses? More specifically, I want to pack small circles in hex and square patters in a larger cicle (https://www.wolframalpha.com/...
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### How to draw a distribution plot (dotplot?) like this in mathematica? [duplicate]

I believe I've seen this answered already here in Stack Exchange but I could not find it again, so here I am asking, hoping that someone knows this other post I am referring to. Here are examples of ...
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### Packed Graph or GraphPlot output with non-square layout?

Graph or GraphPlot produce square layouts for disconnected graphs: Graph[Table[i -> Mod[i^3, 100], {i, 1, 100}]] I´d like to get a rectangular layout with e.g....
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