Questions about random number generation and the properties of numbers so generated.

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30
votes
6answers
2k 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 ...
11
votes
1answer
306 views

Are there rules of thumb for knowing when RandomVariate is more efficient than RandomReal?

Please consider the following: From a fresh Mathematica kernel, RandomVariate is more efficient for NormalDistribution but ...
4
votes
1answer
298 views

How to fix errors in Gram-Schmidt process when using random vectors?

I first make a function to get a random vector on unit sphere in a swath around the equator. That is what the parameter $\gamma$ controls; if $\gamma = 1/2$, the vectors can be chosen anywhere on the ...
6
votes
2answers
467 views

Generate Random Text within a Rectangle

I would like to generate images such as the four below. That is: some text of different length fit within a Rectangle[] using ...
3
votes
2answers
889 views

creating vectors with normal distribution of lengths

First consider vectors of unit length, say on the unit sphere. Now I want to give some magnitude to these vectors and I want the magnitude to be chosen from the normal distribution. In one dimension ...
10
votes
2answers
569 views

Creating randomly oriented planes

I would like to create randomly oriented planes. This is how I'm attempting to do that: I create a 2 random unit vectors, $\mathbf{v}_1$, and $\mathbf{v}_2$, in the $x$-$y$ plane I assume that if I ...
3
votes
1answer
171 views

Generate a new output using Manipulate

Thanks to methods found in the below, I was able to assemble those elements : Tile image on specific location without space between them How to combine images with the same dimensions in a grid? ...
22
votes
3answers
654 views

Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
14
votes
3answers
3k views

How to generate random directed acyclic graphs?

How to programmatically build random directed acyclic graphs (DAG)? I know about the AcyclicGraphQ predicate and the ...