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Questions tagged [visualization]

Data visualization is the study of the visual representation of data, meaning "information that has been abstracted in some schematic form, including attributes or variables for the units of information"

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64
votes
3answers
3k views

Homotopy Visualization

I noticed that both the lower cased 'i' and the Apple logo  are topologically equivalent to the disjoint union of two closed discs. I'd like to animate a homotopy from the left to the right, can ...
64
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7answers
9k views

How to plot Venn diagrams with Mathematica?

How does one plot Venn diagrams with Mathematica? I've searched quite a bit and I've found one source at MathWorld which provides the source code for doing them. But I don't understand this code, can ...
54
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4answers
4k views

Is there an easy way to use Matteo Niccoli's perceptual color maps for 2D plots in Mathematica?

I have been using the ubiquitous Jet color palette for 2D plots for some time now, and don't really care for it. Then I came across the series of blog posts, The rainbow is dead...long live the ...
50
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5answers
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Creating ghost trail effects

Does anyone know how to create a ghost trail effect? For a simple example look at this screenshot: You can find the actual animation here. What I would ultimately like to see it happen is to make the ...
50
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4answers
5k views

How to visualize 3D fit

I have a data set of x,y,z values and I fit a function of x,y to the data. This works, but I can't come up with a nice way to ...
49
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1answer
2k views

Constructing election cartograms?

I found this pretty neat page showing cartograms for the US elections and I don't really know how to get started doing these graphics in Mathematica. For those who don't know, a cartogram is a map in ...
48
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2answers
4k views

How to show solid bodies using volumetric rendering?

Note: This question was asked when Mathematica 8 was latest release. Version 9 has built-in support for volume rendering through Image3D. There's an example on ...
48
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1answer
2k views

How to construct a treemap using non-rectangles?

I've written the standard version of a tree map (a graphic that shows nested data) and I'm looking to improve on this layout by switching to different types of polygons or perhaps circles. Can anyone ...
47
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6answers
5k views

ColorData[“VisibleSpectrum”] is wrong?

Bug introduced in 10.0 or earlier and fixed in 11.1 I am trying to visualize the visible spectrum using the built-in ColorData["VisibleSpectrum"] function which "...
47
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2answers
3k views

Möbius transformations revealed

Möbius Transformations Revealed is a short video that vividly illustrates the simplicity of Möbius transformations when viewed as rigid motions of the Riemann sphere. It was one of the winners in the ...
46
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3answers
2k views

Visualizing the difference between two sequences (strings)

I'm trying to develop a way of comparing two sequences (probably originally text, such as text writing or source code, possibly converted to lists). As a familiar example, consider the revisions ...
45
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3answers
2k views

Implementing hexagon binning in mathematica

Hexagon bin plots are a useful way of visualising large datasets of bivariate data. Here are a few examples: With bin frequency indicated by grey level... ..and by glyph size There are packages for ...
43
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7answers
5k views

How to plot contours on the faces of a cube

I'm trying to plot contours of a function f[x,y,z] on the faces of a cube as the example below, which represents the domain of this function. Is there a way to do ...
41
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1answer
8k views

How to visualize Riemann surfaces?

In WolframAlpha we can easily visualize Riemann surfaces of arbitrary functions, can we plot the Riemann surface of an arbitrary function using Mathematica and ...
40
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2answers
6k views

How to build a bvh (a motion capture file format) player in Mathematica?

How to build a bvh player that can be used to visualize human motions in Mathematica? Any idea or sample code would be appreciated. ...
36
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2answers
2k views

How can I use Kenneth Moreland's “Diverging Color Maps for Scientific Visualization” in plots?

I often want to plot two dimensional data that is centered around zero (for me, this is usually a 2D optical spectroscopy signal, but there are other cases), and the MATLAB "Jet" color scheme is ...
36
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1answer
621 views

Visualizing Type System Operations

With the introduction of Dataset in version 10, Mathematica acquired a static type-checking subsystem. A fair number of dataset-related questions here on MSE ...
35
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4answers
4k views

How to create a wind rose with Mathematica?

I am trying to plot wind rose in Mathematica, but have no idea how to do this. Any suggestions ?
35
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2answers
3k views

Create the source image for this cool animated illusion

Have a look at this very awesome video: https://www.youtube.com/watch?v=lvvcRdwNhGM You have a vertically discretized image, which is composed of 5 or 6 images, which are shifted by an increment, as ...
35
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2answers
1k views

General techniques for creating complex animations

I love good animations of abstract concepts, and when I try to create them myself, I prefer doing so in code to make sure they are exact (and because some things are just way too fiddly to do by hand)....
33
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3answers
2k views

Visualize an irrational number

I would like to visualize an irrational number like the square root of 2 with Mathematica. I found this visualization of Pi in the internet and wonder how this ...
32
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5answers
8k views

Showing the correlation of two variables using a plot

I have a list of $\{x_i,y_i\}$ pairs and I want to show that $x_i$'s and $y_i$'s have positive correlation. The result of ...
31
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1answer
1k views

Visual representation of a Ranking over time (image provided)

[Disclaimer: I initially posted this question on stackOverflow 2 months ago and think it might be better suited for this forum (link to original question)] The graph below shows a ranking of ...
30
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2answers
1k views

How to Make a Sankey Diagram

I have two lists start = {{1},{1},{1},{2},{3},{1}} end = {{1},{2},{2},{3},{3},{1}} And I want to create a Sankey diagram. Which looks something like So, ...
29
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2answers
4k views

Visualizing vector spherical harmonics

I have painstakingly derived the vector-spherical harmonics $\mathbf{V}_{J,\,M}^\ell(\theta, \phi)$, which are the generalization of ordinary spherical harmonics $Y_\ell^m(\theta, \phi)$ to vector ...
26
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7answers
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Graphical representation of a moving sound source

Some explanation since I have got a specific and another more open-ended question: I used two microphones in a 90° arrangement (see picture below) to capture sound from a source moving around the room ...
26
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6answers
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Using ListPointPlot3D to simulate 2D plots moving in time

I wrote a 1D solver for the heat equation $u_t=u_{xx}$, and I can animate the solution using normal ListPlot command, where the x-axis is the rod length, and the y-...
26
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4answers
1k views

How can the opacity of a dense data set be automatically chosen?

The problem In a dense data set plotted with opaque points, data points can pile on top of each other. This can cause serious problems with the interpretation of the plots. I'll use as an example a ...
25
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2answers
3k views

How can we produce a graph layout with hierarchical edge bundling in Mathematica?

I'm looking to reproduce the types of graph layout that are possible in D3 (http://bl.ocks.org/mbostock/7607999) in Mathematica. Since Mathematica doesn't explicitly support force directed edge ...
25
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3answers
5k views

Visualizing a Complex Vector Field near Poles

I've been playing around with a visualization technique for complex functions where one views the function $f: \mathbb{C} \rightarrow \mathbb{C}$ as the vector field $f: \mathbb{R^2} \rightarrow \...
24
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3answers
2k views

Plot 3D model of DNA in Mathematica

My friend asked me if we can plot a 3D model of DNA (deoxyribonucleic acid) in Mathematica. However, I am not really familiar with this and I don't know if Mathematica can do this. Could you answer ...
24
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3answers
2k views

Visualisation of a recursive function

Is there a way to nicely visualize recursive functions? (diagrams/plots) More specifically I'm looking for a way to make contrast (visually) between e.g. the cosine function which if continuously ...
24
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3answers
3k views

How can I make a heatmap of a days in year?

I know Mathematica has a ListPlot for time series but does it have a function for visualizing a list of dates as a heat map like this: This idea is from D3, check it out here.
24
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2answers
1k views

How to plot planar graphs in a visually pleasing way?

Cross posted to Wolfram Community Mathematica has a layout algorithm to plot planar graphs without edge crossings. This typically produces an ugly triangular layout where some vertices and edges are ...
24
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0answers
805 views

How can I trace a functional expression's evaluation visually?

Ok, so the goal is to visualize the execution of this expression foo /@ {3 + 1, bar /@ {1 + 2, {4 + 7}}} in the following fashion using nested rectangles with ...
23
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2answers
883 views

Better way to visualize cylinder puzzle solution

The above puzzle has been a recent source of amusement in my clique. I decided to provide a visualization to motivate solution (here): My code: ...
23
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1answer
807 views

Import and Plot Git Commit History

What might be the easiest to import and plot all commit history for a github project? I'm looking for something similar to the following.
23
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4answers
613 views

How can I regroup elements in a list into a tree based on their values?

I have a list of elements in an outline, here is an example that is only 3 levels deep: ...
22
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5answers
12k views

How do I plot a plane EM wave?

I would like to display an electromagnetic (EM) wave. I have written code that works, but it does not "shade" the area between the graph and the axes. Both the ...
22
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2answers
3k views

Weather Maps with Mathematica

I've been trying to set up a weather map with Mathematica similar to what NOAA publishes in their website. So far I've been successful to bring the data over and extend it across the whole picture ...
22
votes
1answer
779 views

How can we create Randolph diagrams in Mathematica?

I have become fascinated with Randolph Diagrams and was wondering how we would create the diagrams from logical sequences using Mathematica? It looks like it would be a combination of logic and ...
21
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5answers
1k views

How to visualize the voting choices in the moderator elections?

I'm trying to use Mathematica to create some visual representations of the votes cast in the recent Mathematica-StackExchange moderator elections. (Not the vote-counting system itself, OpenSTV, but ...
21
votes
5answers
6k views

Spherical density plot of data set

I have a somewhat large number of 3-dimensional unit vectors ( ~ 100 000 unit vectors), and I am trying to visualize their distribution. First thing I tried was ...
21
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3answers
13k views

Plotting vectors originating from the origin in 3D

I have an array of data with 3D elements. Ex: x = {{1,2,3}, {3,4,5}, {5,6,7}}. I want to show this data in 3 dimensions, such that each point in the space is shown ...
21
votes
1answer
640 views

Gravatars/identicons with Mathematica

The default avatar/identicon is based on an MD5 hash of your e-mail address. With some e-mail providers (e.g., GMail) the address gmailuser+foo@gmail.com is still ...
21
votes
1answer
746 views

Mouse motion heat map - live visualization and analysis

Mouse motion heat map is an great way to study spatial attention distribution, styles of movement, reaction, etc. I am trying to design a code that visualizes such heat map. The requirements: 1) It ...
20
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2answers
2k views

Higher order periodic interpolation (curve fitting)

I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
20
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3answers
2k views

Is it possible to position ticklabels on the negative y axis on its right side?

Is it possible to position ticklabels on negative $y$ axis on its right side? Ticklabels on positive $y$ axis should remain as usual:
20
votes
2answers
925 views

Wind Map Artwork

I would like some help generating an image like the one seen below. The image above is an art piece called Wind Map by artists Fernanda Viégas and Martin Wattenberg. I would like to take wind data ...
20
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1answer
249 views

Systemic bugs in GraphPlot and related functions such as TreePlot and TreeForm

Bug introduced in 7.0.1 or earlier and fixed in 10.3.0 I believe I have come across a rather curious bug in TreeForm: ...