Create/Draw a Binary Fractal Tree with plotly in R

fractal_tree.R

# Create/Draw a Binary Fractal Tree

library(plotly)

# basic strucure for line shape in plotly
base_line = list(
  type = "line",
  line = list(color = "black"),
  xref = "x",
  yref = "y",
  x0   = NA,
  x1   = NA,
  y0   = NA,
  y1   = NA
)

# create a plotly line shape given start and end coords
create_line = function(p1, p2) {
  base_line[['x0']] = p1[1]
  base_line[['y0']] = p1[2]
  base_line[['x1']] = p2[1]
  base_line[['y1']] = p2[2]

  return(base_line)
}

# create line segment from (0, 0) to (0, len) to be trunk of fractal tree
create_trunk = function(len = 1) {
  l = create_line(c(0, 0), c(0, len))
  return(list(points = c(0, len),
              branches = list(l)))
}

# creates end point of line segment to satisfy length and
# angle inputs from given start coord
gen_end_point = function(xy, len = 5, theta = 45) {
  dy = sin(theta) * len
  dx = cos(theta) * len

  newx = xy[1] + dx
  newy = xy[2] + dy
  return(c(newx, newy))
}

# create a single branch of fractal tree
# returns branch endpoint coords and a plotly line shape to represent branch
branch = function(xy, angle_in, delta_angle, len) {
  end_point = gen_end_point(xy, len = len, theta = angle_in + delta_angle)
  line_shape = create_line(xy, end_point)
  return(list(points=end_point, branches=list(line_shape)))
}

# helper function to aggregate branch objects into single branch object
collect_branches = function(branch1, branch2) {
  collected_points = rbind(branch1$points, branch2$points)
  collected_branches = c(branch1$branches, branch2$branches)
  return(list(points=collected_points, branches=collected_branches))
}

# recursively create fractal tree branches
create_branches = function(xy,
                           angle_in = pi / 2,
                           delta_angle = pi / 8,
                           len = 1,
                           min_len = 0.01,
                           len_decay = 0.2) {
  if (len < min_len) {
    return(NULL)
  } else {
    branch_left = branch(xy, angle_in, delta_angle, len)
    subranches_left = create_branches(branch_left$points,
                                      angle_in = angle_in + delta_angle,
                                      delta_angle = delta_angle,
                                      len = len * len_decay,
                                      min_len = min_len,
                                      len_decay = len_decay)
    branches_left = collect_branches(branch_left, subranches_left)

    branch_right = branch(xy, angle_in, -delta_angle, len)
    subranches_right = create_branches(branch_right$points,
                                       angle_in = angle_in - delta_angle,
                                       delta_angle = delta_angle,
                                       len = len * len_decay,
                                       min_len = min_len,
                                       len_decay = len_decay)
    branches_right = collect_branches(branch_right, subranches_right)

    return(collect_branches(branches_left, branches_right))
  }

}

# create and draw binary fractal tree
draw_fractal_tree = function(trunk_len=10,
                             delta_angle = pi / 8,
                             len_decay=0.7,
                             min_len=0.25) {

  trunk = create_trunk(trunk_len)
  branches = create_branches(trunk$points,
                             delta_angle =delta_angle,
                             len = trunk_len * len_decay,
                             min_len = min_len,
                             len_decay = len_decay)

  tree = collect_branches(trunk, branches)
  tree_points_df = as.data.frame(tree$points)
  names(tree_points_df) = c('x', 'y')

  null_axis = list(
    title = '',
    zeroline = FALSE,
    showline = FALSE,
    showticklabels = FALSE,
    showgrid = FALSE
  )

  plot_ly(
    tree_points_df,
    x =  ~ x,
    y =  ~ y,
    type = 'scatter',
    mode = 'markers',
    color =  ~ x,
    colors = 'Spectral',
    hoverinfo = "none",
    showlegend = FALSE
  ) %>%
    layout(shapes = tree$branches,
           xaxis = null_axis,
           yaxis = null_axis) %>%
    hide_colorbar() %>%
    config(displayModeBar = FALSE)
}

# example usage/output
draw_fractal_tree(delta_angle = pi / 2)
draw_fractal_tree(delta_angle = pi / 4)
draw_fractal_tree(delta_angle = pi / 8)
draw_fractal_tree(delta_angle = pi / 16)

Example output