# Tagged Questions

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

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 ...
1answer
3k views

### RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
3answers
1k 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 ...
1answer
1k views

### Uniformly distributed n-dimensional probability vectors over a simplex

What's the right way to generate a random probability vector $p={p_1,\ldots,p_n} \in {(0,1)}^n$ where $\sum_i p_i=1$, uniformly distributed over the $(n-1)$-dimensional simplex? What I have is ...
5answers
812 views

### obtaining random element of a set given by multiple inequalities

I try to obtain random elements from a set given by multiple inequalities. This is of general interest to me, but let me present one example here: I have multiple inequalities specifying half spaces ...
8answers
2k views

### How to generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
9answers
11k views

### How to create animated snowfall?

Well, the title is self-explanatory. What sorts of snowfall can we generate using Mathematica? There are two options I suggest to consider: 1) Continuous GIF animations with smallest possible number ...
4answers
3k views

### Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. Attempt I wrote the ...
6answers
2k views

### Vectors with a certain magnitude in Mathematica

For a user-specified magnitude, is there a way to have Mathematica produce any 3D vector with that magnitude?
5answers
3k views

### 2D random walk within a bounded area

I want to simulate a random walk on two dimension in a bounded area such as a square or circle. I am thinking of using If statement to define a boundary. Is there a ...
3answers
6k views

### How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
3answers
2k views

### Can Mathematica's random number generation be improved?

Performance on Random Number generation is intolerable. Whenever you need many deviates from the same distribution but with different parameters it takes forever. Here is a thread on Poisson ...
5answers
4k views

### Distribution of random points in 3D space to simulate the Crab Nebula

I'm generating some 3D models of planetary nebulae and supernova remnants for Celestia, a free OpenGL astronomy software. Currently, I know how to do it with random points inside a spherical shell. ...
1answer
540 views

### Simulating Theatre puzzle

I have been trying to simulate the process of the theatre puzzle from the Joy of X (Strogatz). The puzzle, and some relevant material are here. My simplistic coding for this process follows: ...
3answers
6k 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 ...
1answer
677 views

### Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
2answers
250 views

### generating randomly oriented non-intersecting cylinders

I could not find anything relevant with "googling" (only this) I can create a set of randomly oriented cylinders (code found here) ...
1answer
797 views

### Randomly selecting elements without repetition

I assigned energy values to each element in the array as per the program of Verbeia. The program looks like this ...
7answers
20k views

### How to generate a random snowflake

'Tis the season... And it's about time I posed my first question on Mathematica Stack Exchange. So, here's an holiday quest for you Graphics (and P-Chem?) gurus. What is your best code for generating ...
3answers
3k views

### Quality of random numbers

Mathematica has several ways of generating random numbers: Congruential, ExtendedCA, Legacy, MersenneTwister, MKL, ParallelGenerator, ParallelMersenneTwister, Rule30CA. For ...
1answer
2k views

### Finding the likeliest path in a Markov process

With Mathematica 9, we have the addition of various processes, among which the discrete Markov process. Given a transition probability matrix m, such a process is ...
3answers
3k views

### Create triangular mesh from random list of points

I have a list of points. I would like to take these points and create a mesh of triangles from them, making sure triangles don't overlap. So here's a list of points: ...
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 $0.7$.
2answers
598 views

### Monte Carlo integration with random numbers generated from a Gaussian distribution

I want to do numerical integration of some functions using the Monte Carlo method. The default setting for the Monte Carlo method is to use a uniform distribution as far as I know. How can I change ...
3answers
473 views

### Turning a set of random walk data 45 degrees

I have a set of data that is just a "random" (generated by me, not by computer) sequence of length 2000 of 1's and (-1)'s. I used it to plot a 1-D random walk where +1 is step up, (-1) is step down, ...
5answers
2k views

### Random numbers that sum up to specific value

I would like to generate a list with random numbers, which add up to a specific value. While[Total[x] == 28, x = RandomInteger[{0, 28}, 5];Print[x]] The random ...
4answers
1k views

### Random real numbers that sum up to specific value [duplicate]

In here, it works with "Integer". What if I want 5 positive real numbers that sum to 1? RandomChoice[IntegerPartitions[100, {5}]]/100. That will work. But only ...
3answers
392 views

### Random non-overlapping disks in a square

I've found a nice code snippet by @belisarius from this question, that I'll reproduce here for reference: ...
1answer
394 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 <...
4answers
672 views

### Why is Poisson Random Deviate Generation so slow?

I am generating Poisson deviates for some numerical work. Mathematica 9.0.1 is very slow in generating these random numbers, as can be seen below. ...
1answer
298 views

### Sample of the random times at which the random walk crosses the boundary

I defined a security boundary for a random walk: ...
5answers
1k views

### Assigning a particular value to array elements

I have an array of 10000 elements. I want to randomly assign energy to these 10000 elements using Gaussian or Exponential distribution, such that each time a particular element is selected its energy ...
4answers
2k views

### Finding the volume of a sphere using the Monte Carlo algorithm

I used the following code to find the volume of the sphere $x^2+y^2+z^2 \leq 1$ in the first octant: ...
4answers
2k views

### 3D Random Walk with Periodic Boundary Conditions

I am working on a 3D random walk with periodic boundary conditions and have written a program that will do this for me, but it is extremely slow. Does anyone have any suggestions on how I could speed ...
2answers
1k views

### Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
3answers
2k views

### Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
5answers
1k views

### Picking random items out of a list only once

I'm trying to create a function that randomly returns a value from a list but remembers the values that have been given before. At the end when the list is empty it should return an empty list. ...
2answers
673 views

### Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
3answers
917 views

### 1D Random Walk variant

I am making a notebook that is a variation to the traditional 1d random walk problem. The normal 1D random walk can be simulated easily by ...
1answer
375 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1answer
258 views

### Why does't SeedRandom work here?

From the docs on SeedRandom, SeedRandom[] resets the generator, using as a seed the time of day and certain attributes of ...
5answers
564 views

### How can I generate and randomly assign color to annular sectors?

How can I generate such an image and fill every annular sector with a random colour?
3answers
441 views

### Assign a randomly generated list to variable

Bug introduced in 10.0.0 and fixed in 10.0.2 I don't know if this is a silly question, but it really baffles me. So please help me understand this behavior. ...
4answers
654 views

### Random sampling of multiple integers with constant sum

I want to build a model of 40 geological layers, assuming each layer has equal chance to be one of the four types of rocks and the four types of rocks have equal chance to appear in any layer. The ...
1answer
851 views

### How do I get a list of unique random integers? Avoiding numbers being drawn twice [duplicate]

I am trying to get a set of random integers for which I used the function RandomInteger[{1, 50}, 5]. That way, however, there is the chance to get doubles such as <...
2answers
525 views

### Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
1answer
1k views

### Add noise (random values) to data

I have a data set(x,y,z) corresponding to a hemisphere, to which I want to add some controlled noise (random values) to make the x,y,z values diverge. data = Flatten[ Table[{i, j, i^2 + j^2}, {i, ...
2answers
111 views

### Sum considers RandomInteger[] as a constant

Perhaps this is expected behavior, but I was kind of surprised by the following: ...
1answer
110 views

### Huge overhead in RandomPoint[ImplicitRegion]

Commenting answers of this question @JasonB noticed the big overhead of RandomPoint ...
3answers
189 views

### Performance on Multinomial Deviate is slow

Most of the time in my program is spent on this single line of code: out = RandomVariate[MultinomialDistribution[nt, tmp]]; ...