Figure 7.7 Coordination in space-time paths

figures

code

This page shows a different set of ‘flockers’ converging in space-time—in fact the same ones that are used on the ‘make your own cover’ page. I’ve provided two plots here, both in colour, and one an interactive 3D plot so you can have a proper look.

Code

library(dplyr)
library(gg3D)
library(plotly)

flockers <- read.table('traces.csv', sep=' ', header = TRUE)

It’s worth noting that plotly rescales all the coordinates here (because I ask it to with asp = 1) but that’s probably best for giving a general impression of the patterns.

Code

plot_ly(group_by(flockers, who), 
        x = ~x, y = ~y, z = ~t, color = ~who, colors = "magma",
        type = 'scatter3d', mode = 'lines', asp = 1, lwd = 0.5)

Not nearly as much fun is the static plot (like the “library in a theme park”, as my favourite cricketer once said).

Code

ggplot(flockers, aes(x = x, y = y, z = t, group = who, color = who)) +
  stat_3D(theta = 135, phi = 35, geom = "path",
          linewidth = 0.35, alpha = 0.75) +
  scale_color_viridis_c(option = "A") +
  coord_equal() +
  theme_void() +
  theme(legend.position = "none")

Code

# License (MIT)
#
# Copyright (c) 2023 David O'Sullivan
#
# Permission is hereby granted, free of charge, to any person
# obtaining a copy of this software and associated documentation
# files (the "Software"), to deal in the Software without restriction,
# including without limitation the rights to use, copy, modify, merge,
# publish, distribute, sublicense, and/or sell copies of the Software,
# and to  permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included
# in all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
# THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
# DEALINGS IN THE SOFTWARE.