# plot_word3D: Plot the 3D fractal containing the chosen word In ChaosGame: Chaos Game

 plot_word3D R Documentation

## Plot the 3D fractal containing the chosen word

### Description

The function allows to enter a word of at least two letters based on which an Iterated Function System with Probabilities (IFSP) is constructed. This IFSP is then used to generate a two-dimensional fractal containing the chosen word infinitely often, which is then projected onto several three-dimensional surfaces. Optionally, the projection is transformed into another fractal with uniform marginals.

### Usage

```plot_word3D(
word = "copula",
R = 20,
plot.rgl = TRUE,
copula = TRUE,
portion = 0.2,
color.rgl.plot = "green2magenta",
plot.surface = "Sphere",
histogram = TRUE,
shift = 1.2,
orbit = 3000,
cex.label = 0.7,
size.lines = 0.1,
Theta = 40,
Phi = 30,
Box = TRUE,
projection = TRUE,
letter_type = 1
)
```

### Arguments

 `word` Word which the fractal should contain infinitely often. `R` Number of runs of the chaos game. `plot.rgl` If `plot.rgl = TRUE` a rgl-plot is generated. Otherwise a scatter-plot with plot3D is produced. `copula` logical. If TRUE the sample is (approximately) probability-integral-transformed. `portion` Portion based on which the empirical distribution functions are calculated, if `copula = TRUE`. `color.rgl.plot` Plotting color/color-range for the rgl-plot. One can choose between `"gray"`, `"blue2green"`, `"green2red"`, `"blue2yellow"`, `"ygobb"`, `"magenta2green"` and `"green2magenta"`. `plot.surface` Three-dimensional surface on which the two-dimensional fractal is projected. Options are `"Sphere"`, `"Helix"`, `"Torus"`, `"EnneperMinimalSurface"` and `"CatalanSurface"`. `histogram` It is an option available only under the rgl-plot option (i.e if `plot.rgl = TRUE`). If `histogram = TRUE`, two-dimensional and one-dimensional marginal histograms are plotted in the rgl-plot. `shift` Distance between letters. `orbit` Number of steps in each run of the chaos game. `cex.label` Font size, for exporting as a pdf or png file (see examples). `size.lines` Line width, for exporting as a pdf or png file (see examples). `Theta` Angles defining the viewing direction. `Theta` gives the azimuthal direction and `Phi` the colatitude in the scatter-plot (see Package plot3D). Can be chosen only under the scatter-plot option (i.e if `plot.rgl = FALSE`). `Phi` Angles defining the viewing direction. `Theta` gives the azimuthal direction and `Phi` the colatitude in the scatter-plot (see Package plot3D). Can be chosen only under the scatter-plot option (i.e if `plot.rgl = FALSE`). `Box` If `TRUE`, axis, two-dimensional projections (if `projection = TRUE`) and marginal histograms are plotted. `projection` An option available only if `Box = TRUE`. If `projection = TRUE`, the two-dimensional projections are plotted together with axis and marginal histograms. `letter_type` integer, which indicates the type of the letters. Options are 1 (default) or 2 (round letters).

### Examples

```# function with a word as input, runs the chaos game,
# calculates the copula transformation and projects the result on a sphere:
# for nice results use, for example, R = 20 and orbit = 3000
# A <- plot_word3D(word = "copula", copula = FALSE, R = 50, orbit = 100)

# further examples:
# projection of the fractal on the Enneper Minimal Surface:
# A <- plot_word3D(word = "copula", R = 75, orbit = 300, copula = FALSE,
#                  plot.surface = "EnneperMinimalSurface", histogram = FALSE)
# same example as before, now with histogram = TRUE
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE,
#                  plot.surface = "EnneperMinimalSurface")
# same example as before (approximately) probability-integral-transformed  (i.e. copula = TRUE)
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = TRUE,
#                   plot.surface = "EnneperMinimalSurface")

# projection of the fractal on a Catalan Surface
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE,
#                  color.rgl.plot = "blue2green", plot.surface = "CatalanSurface")

# projection of the fractal on a Helix
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE,
#                  color.rgl.plot = "green2red", plot.surface = "Helix")

# projection of the fractal on a Torus
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE,
#                  color.rgl.plot = "blue2yellow", plot.surface = "Torus")

# projection of the fractal on a Sphere
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE,
#                  color.rgl.plot = "ygobb", plot.surface = "Sphere")
# Sphere (approximately) probability-integral-transformed (i.e. copula = TRUE)
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = TRUE,
#                  color.rgl.plot = "ygobb", plot.surface = "Sphere")

# scatter-plot with plot3D (i.e. plot.rgl = FALSE) for exporting as a pdf file
# pdf(file = "Sphere.pdf", width = 30, height = 25)
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE, plot.rgl = FALSE,
#                  plot.surface = "Sphere", cex.label = 1.8, size.lines = 0.001)
# dev.off()

#' # scatter-plot with plot3D (i.e. plot.rgl = FALSE) for exporting as a png file
# png(file = "Sphere.png", width = 5000, height = 4000)
# A <- plot_word3D(word = "copula", R = 100, orbit = 300, copula = FALSE, plot.rgl = FALSE,
#                  plot.surface = "Sphere", cex.label = 5, size.lines = 2)
# dev.off()
```

ChaosGame documentation built on Dec. 9, 2022, 5:08 p.m.