Dragon Curve#

Download this notebook from GitHub (right-click to download).

Dragon curve example from the L-systems topic notebook in examples/topics/geometry.

Most examples work across multiple plotting backends, this example is also available for:

import numpy as np

import holoviews as hv
from holoviews import opts

hv.extension('bokeh')

L-system definition#

The following class is a simplified version of the approach used in the L-systems notebook, made specifically for plotting the Dragon Curve.

class DragonCurve:
    """L-system agent that follows rules to generate the Dragon Curve"""

    initial ='FX'
    productions = {'X':'X+YF+', 'Y':'-FX-Y'}
    dragon_rules = {'F': lambda t,d,a: t.forward(d),
                    'B': lambda t,d,a: t.back(d),
                    '+': lambda t,d,a: t.rotate(-a),
                    '-': lambda t,d,a: t.rotate(a),
                    'X':lambda t,d,a: None,
                    'Y':lambda t,d,a: None }

    def __init__(self, x=0,y=0, iterations=1):
        self.heading = 0
        self.distance = 5
        self.angle = 90
        self.x, self.y = x,y
        self.trace = [(self.x, self.y)]
        self.process(self.expand(iterations), self.distance, self.angle)

    def process(self, instructions, distance, angle):
        for i in instructions:
            self.dragon_rules[i](self, distance, angle)

    def expand(self, iterations):
        """Expand an initial symbol with the given production rules"""
        expansion = self.initial

        for _ in range(iterations):
            intermediate = ""
            for ch in expansion:
                intermediate = intermediate + self.productions.get(ch,ch)
            expansion = intermediate
        return expansion

    def forward(self, distance):
        self.x += np.cos(2*np.pi * self.heading/360.0)
        self.y += np.sin(2*np.pi * self.heading/360.0)
        self.trace.append((self.x,self.y))

    def rotate(self, angle):
        self.heading += angle

    def back(self, distance):
        self.heading += 180
        self.forward(distance)
        self.heading += 180

    @property
    def path(self):
        return hv.Path([self.trace])

Plot#

hmap = hv.HoloMap(kdims='Iteration')
for i in range(7,17):
    hmap[i] = DragonCurve(-200, 0, i).path

hmap.opts(
    opts.Path(axiswise=False, color='black', line_width=1,
              title='', xaxis=None, yaxis=None, framewise=True))
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