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This repository contains the raw data and code for Carr, Smith, Cornish, and Kirby (2016) -- three experiments looking at the evolution of language structure in an open-ended meaning space through iterated learning. See the paper for full details.

Carr, J. W., Smith, K., Cornish, H., & Kirby, S. (2017). The cultural evolution of structured languages in an open-ended, continuous world. Cognitive Science, 41, 892-923. doi:10.1111/cogs.12371

Repository Content

The repository contains the following directories:

  • /analysis: Python code for analyzing the data.

  • /data: Plain text files containing the data for the three experiments and the two rating tasks.

  • /experiment: HTML, JavaScript, and PHP code for running the experiments.

  • /rating_tasks: HTML, JavaScript, and PHP code for running the online rating tasks.

Analytical Code

The /analysis directory contains Python code for analyzing the three experiments and the two rating tasks. The Python modules are listed below with a brief description. See below for examples of how to use the code.

  • Basic functions called from various other modules; mainly used for loading in data.

  • Functions for retrieving and plotting communicative accuracy and communicative error results, and for analyzing the data from the second online ratings task.

  • Functions for retrieving and plotting expressivity results.

  • Functions for computing the geometrical dissimilarity between pairs of triangles.

  • Various basic geometrical functions for dealing with triangles.

  • Code for producing an initial Generation-0 set file used to initiate a chain.

  • Module for computing Krippendorff’s alpha coefficient. Adapted from:

  • Functions for generating an initial Generation-0 randomized language.

  • Module for running a Mantel test on two distance matrices.

  • Module for computing an MDS solution to the naïve raters’ dissimilarity ratings and producing Voronoi-tessellated plots and triangle graphics.

  • Module for running Page’s test.

  • Module that interfaces with Matplotlib for producing plots of a consistent style.

  • Functions for analyzing the dissimilarity data from the naïve raters and forming a distance matrix that can be used by other modules.

  • Functions for generating the stimulus sets for naïve raters in Tasks 1 and 2 to work on.

  • Functions for analyzing sound symbolism.

  • Functions for computing and plotting structure results.

  • Module for measuring sublexical structure.

  • A simple class for drawing polygons and saving to an SVG file.

  • Functions for computing and plotting transmission error results.

  • Functions for transforming a string into a synthesized vocalization using the Apple MacinTalk speech synthesizer.

  • Module for creating a Voronoi tessellation. Adapted from:

  • Functions for calculating average word length.

Raw Data

The /data directory contains subdirectories for the three experiments and the two rating tasks. The experiment directories are further divided into subdirectories for each chain.

Experiment data

The directory for each chain contains 32 plain text files. The initial number in the filename refers to the generation number, which is followed by d (dynamic set), s (static set), or log (log file). Dynamic set files list the 48 words used by the participant to label the dynamic set, alongside coordinates for the corresponding triangles (x-coordinate and y-coordinate for vertices 1, 2, and 3; vertex 1 is always the orienting spot), and a timestamp for when the response was submitted. The lines of the file are in order of presentation. Static set files follow the same organization, except they are ordered according to an arbitrary number assigned to each triangle in the static set and contain an additional column which gives the order of presentation. The order of static set files is the same for all participants, meaning that the strings in consecutive static set files can be compared directly.

Log files contain some header information, including a timestamp marking the beginning of the training phase, followed by a long sequence that describes the order in which items were presented throughout the experiment (TR = training item, MT = mini-test item, TS-d = test on a dynamic set item, TS-s = test on a static set item). This sequence is followed by the mini-test results (target answer and typed answer separated by tabs) and finally a timestamp for the end of the experiment. These files are exactly the same for Experiment 2, except the log file contains an additional line near the bottom which gives a count of the number of times the participant was told to enter a different word during their test phase.

The Experiment 3 data (42 files per chain) is organized in the same way as described above with the following two exceptions: (1) the dynamic and static set files contain additional columns giving the coordinates of the triangle selected from the matcher array, and (2) there are two log files per generation marked with SubA and SubB for subjects A and B respectively. Subject A is always the first participant to be the director and labels the dynamic set; subject B always labels the static set.

Rating task data

The /task_1 directory contains 96 plain text files, one for each of the participants who completed the first dissimilarity rating task. The filename is a unique “rater ID” used to identify participants. The first line gives the current trial number (the task is complete, so this will always read 151), the direction in which the sliding scale was oriented (L = very similar on the left; R = very similar on the right), the participant’s IP address (all IP addresses have been concealed), and a Unix timestamp for the time the task was started. The subsequent lines give the results for each of the 150 rating trials. The first six trials are practice trials; in addition, three reliability trials are randomly interspersed among the normal trials. Column 1 gives a reference number for the triangle in the static set presented on the left; column 2 gives the reference number for the triangle presented on the right; column 3 gives the participant’s rating on the 1,000 point scale (0 is always very similar and 1000 is always very dissimilar regardless of the direction of the sliding scale); and column 4 gives a Unix timestamp for the time the rating was submitted. Negative reference numbers refer to a small fixed set of triangles used only in practice and reliability trials. The final line in the file is a unique code generated at the time the participant finished the task allowing him or her to collect payment. In some cases, the rating is given as undefined; this was caused by a browser compatibility issue that was later fixed.

The /task_2 directory contains 184 files, one for each of the participants who completed the second dissimilarity rating task. The contents of the files are organized in the same way as described above with the following exceptions: (1) Task 2 is comprised of 135 or 136 trials rather than 150, and (2) the coordinates of each triangle are given in full for each trial rather then represented by reference numbers, since the triangles rated in this task are not drawn from a fixed set as in the case of Task 1.

Replicating the Reported Results

All analytical code is written in Python and has only been tested under version 2.7 of the language. The following nonstandard libraries are used extensively throughout the code and should be installed first (if not already available):

All analyses were performed on OS X El Capitan with up-to-date versions of the above libraries. These instructions are intended to get you started and do not cover the use of every function in every module. They begin with the assumption that you have cd’d into the /flatlanders/analysis directory and opened a Python interpreter, e.g.:

$ cd flatlanders/analysis/
$ python


The following commands are used to import the expressivity module and load in the expressivity data for the dynamic and static sets of Experiment 1:

import expressivity
E1_exp_dynamic = expressivity.experiment_results(1, set_type='d')
E1_exp_static = expressivity.experiment_results(1, set_type='s')

The variables E1_exp_dynamic and E1_exp_static that you have just created are dictionaries containing the expressivity data and other parameters. To get the results for Experiment 2 or 3, change the 1s above to 2s or 3s. To get expressivity results for the union of the dynamic and static set, change the set_type argument to 'c'. To produce a plot, first import the plot module and initialize a Plot object:

import plot
E1_expressivity_plot = plot.Plot(2, 1, 5.5, 2.5)

In this case we are creating a 5.5×2.5 in. multipanel plot with two columns and one row. You can then pass in the dictionaries generated above using the add() method of the Plot object:


Finally, call the make() method to save a PDF:


By default this will save the plot to your desktop as plot.pdf. This can be changed by passing a filename and/or directory, e.g.:

E1_expressivity_plot.make('E1_expressivity', '/Users/jon/')


The following commands are used to import the structure module and compute the structure and sublexical structure results for Experiment 1.

import structure
E1_str = structure.experiment_results(1, permutations=1000)
E1_sub = structure.experiment_results(1, permutations=1000, sublexical=True)

The results reported in the paper are based on 100,000 permutations. However, 1,000 should be sufficient to replicate the results quickly. N.B., the computation of the measure of sublexical structure is around an order of magnitude slower than the measure of general structure. To plot the results, customize the instructions above.

Transmission error

The following commands are used to import the transmission_error module and compute the results for Experiment 1.

import transmission_error
E1_trans_error = transmission_error.experiment_results(1)

Sound symbolism

The following commands are used to import the sound_symbolism module and compute the shape- and size-based sound symbolism results for Experiment 1.

import sound_symbolism
E1_shape = sound_symbolism.experiment_results(1, symbolism='shape')
E1_size = sound_symbolism.experiment_results(1, symbolism='size')

Communicative accuracy

The following commands are used to import the communication module and compute the communicative accuracy and error results for Experiment 3 (n.b., communication only applies to Experiment 3).

import communication
E3_comm_acc = communication.accuracy_results()
E3_comm_err = communication.error_results()

Page’s test

To run Page’s test on any of the data, import the Page module and pass one of the data dictionaries that was created above to the test function. For example, to run Page’s test on the results for structure that we generated above, run:

import Page

MDS plots

The MDS plots and triangle visualizations are produced using the code in This module requires two nonstandard libraries to be installed:

The following generates a graphic for Generation 10 in Chain A with the default parameters:

import mds
mds.plot('A', 10)

N.B., this will not produce the same set of colors shown in the paper; a unique color palette is determined on each run. To get multiple color candidates set the colour_candidates argument to the number of candidates you want and then pick your favorite. To generate plots for an entire chain or experiment, use one of the following:


The plot, plot_chain, and plot_experiment functions can take a variety of arguments to further refine the plots:

  • chain_wide_palette (Boolean) determines whether the color palette is selected based on the string distances across an entire chain or within each generation. Setting this to True is useful if you want to be able to compare across generations. Applies only to plot_chain() and plot_experiment().

  • join_contiguous_cells (Boolean) joins together cells that form a continuous region of one color (this does not always work correctly, so use with caution).

  • label_cells (Boolean) adds string labels to the Voronoi cells.

  • random_seed (int) allows you to manually specify an integer to seed the random number generator. This is useful if you want to reproduce a particular color palette. If no integer is specified a seed is chosen at random.

  • save_location (string) specifies a path where the plot(s) should be saved. If none is specified, plots will be saved to your desktop.

  • show_prototypes (Boolean) adds prototype triangles to the triangle graphics.

  • spectrum (list of two floats in [0, 1]) determines how much of the saturation spectrum to use (in the case of HSB) or how much of the red, green, and blue colors to use (in the case of RGB). This makes it possible to avoid extremely light and/or extremely dark colors. Default is [0.5, 1.0], which should be suitable for HSB. For RGB, a range like [0.1, 0.9] will be more suitable.

  • use_rgb (Boolean) allows you to use RGB (red, green, blue) color space instead of HSB to determine the colors in the color palette. This uses a three-dimensional MDS solution, so may offer a better representation of the string space, but it may also be harder to interpret.

When the plot(s) are saved, the random seed integer is appended to the file or directory name so that you can reproduce the plot(s) at a later time.

Geometrical measure of triangle dissimilarity

The code for computing a geometrical measure of dissimilarity between triangles is contained in When this module is run, it automatically computes distance matrices for all 15 combinations of the four geometrical features and stores them in a list called all_combination_matrices. The last item in that list, all_combination_matrices[14], is the combination of all four features (i.e., Type 15, thus index 14). To plot the Experiment 1 results for structure using the combination of all four features, you can simply pass that matrix to the structure module, which overrides the use of the human dissimilarity ratings:

import geometrical_distance
import structure
E1_str_geo = structure.experiment_results(1, meaning_distances=geometrical_distance.all_combination_matrices[14])

To compare the three experiments in terms of this measure of structure, compute the structure results for the other two experiments:

E2_str_geo = structure.experiment_results(2, meaning_distances=geometrical_distance.all_combination_matrices[14])
E3_str_geo = structure.experiment_results(3, meaning_distances=geometrical_distance.all_combination_matrices[14])

and then plot the results in a 3×1 multipanel plot:

import plot
geo_plot = plot.Plot(3, 1, 5.5, 2.5)
geo_plot.add([E1_str_geo, E2_str_geo, E3_str_geo])
geo_plot.make('geo_structure', per_column_legend=True)


Unless otherwise noted, all code in this repository is licensed under the terms of the MIT License.


Experiments and analyses for exploring the emergence of structured languages under an open-ended meaning space







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