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

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1
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1answer
185 views

packing of smaller spheres onto a bigger one

I want to estimate the maximum number of smaller spheres (of known constant radius, r) that can closely pack around a bigger sphere (of radius, providing R >= r). It would be much appreciated if ...
2
votes
0answers
88 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/...
0
votes
0answers
51 views

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 ...
6
votes
3answers
429 views

find the maximum number of not intersecting circles inside an ellipse

$Version "10.3.0 for Linux x86 (64-bit) (October 9, 2015)" (Sequel to 98724 and 99345) (I use codes originally created by Andy Ross, ybeltukov and J.M.). I ...
0
votes
0answers
29 views

How can I avoid to define public all methods in a package [duplicate]

If I have to code a Package and these package use a lot of functions and variables. In spite of, using in every call of function or variable with namePackage ...
4
votes
0answers
125 views

cut and project tilings — Amman Beenker tilings

A certain research paper gives a recipe for building Amman-Beenker tilings as a special type of cut-and-project algorithm. The result is usually a pleasant kind of aperiodic tiling shape. The ...
8
votes
1answer
602 views

How to generate nonperiodic tilings?

I need to generate nonperiodic tilings which are similar to the attached figure (kite-domino tiling). I was thinking the code is similar to the code for the Penrose tiling. However, that code is too ...
6
votes
2answers
860 views

Distribution of 10 points within a unit square

Related to some packing problems, following problem arose: Distribute 10 points within a square of sides 1, so that minimal distance between them is maximized. With the help of random simulation, or ...
24
votes
4answers
1k views

Implementing a Beeswarm plot in Mathematica

I am looking for a Beeswarm plot implementation in Mathematica. Consider the following data: ...
102
votes
7answers
9k views

Generating visually pleasing circle packs

EDIT: (my conclusion and thank you note) I want to thank you all guys for this unexpected intellectual and artistic journey. Hope you had fun and enjoyed it the same as I did. I would like to ...
5
votes
1answer
803 views

Packing squares into a circle

I am currently trying to solve and understand a problem about packing the maximum of squares into a circle. What I am trying to do, is to calculate the maximum number of variable sized squares (with ...
10
votes
1answer
360 views

Efficiently filling area with disks located at certain points

Starting from a set of points, I want to fill an area using disks. Each disk's center should be one of the points and the disks should not overlap. I've managed to write a function that, given a list ...
10
votes
3answers
3k views

Randomly packing spheres of fixed radius within a cube

How can I have Mathematica randomly place spheres in a cube so they won't overlap? The cube is $20 \times 20 \times 20$, and the spheres have a radius of $0.7$.
28
votes
2answers
1k views

How can I pack circles of different sizes into a spiral?

Given a list of circles of different areas, I need to arrange them tangentially in order of increasing area and spiraling outward. An example of the type of packing I'm attempting is shown by the ...
38
votes
3answers
1k views

Tiling a square

I wondered if there was a way to automate the process of finding a way to tile a tile into a square. The idea is to represent the tile with a matrix of $0$s for blank space and $1$s for filled spaces ...
37
votes
7answers
4k views

Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
22
votes
2answers
469 views

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....
126
votes
4answers
18k views

How to create word clouds?

Word clouds are rather useless fancy and visually appealing plots, where words are plotted with different sizes according to their frequency in a corpus. Many applications exist out there (Wordle, ...