fractals.koch_snowflake
=======================

.. py:module:: fractals.koch_snowflake

.. autoapi-nested-parse::

   Description
       The Koch snowflake is a fractal curve and one of the earliest fractals to
       have been described. The Koch snowflake can be built up iteratively, in a
       sequence of stages. The first stage is an equilateral triangle, and each
       successive stage is formed by adding outward bends to each side of the
       previous stage, making smaller equilateral triangles.
       This can be achieved through the following steps for each line:
           1. divide the line segment into three segments of equal length.
           2. draw an equilateral triangle that has the middle segment from step 1
           as its base and points outward.
           3. remove the line segment that is the base of the triangle from step 2.
       (description adapted from https://en.wikipedia.org/wiki/Koch_snowflake )
       (for a more detailed explanation and an implementation in the
       Processing language, see  https://natureofcode.com/book/chapter-8-fractals/
       #84-the-koch-curve-and-the-arraylist-technique )

   Requirements (pip):
       - matplotlib
       - numpy



Attributes
----------

.. autoapisummary::

   fractals.koch_snowflake.INITIAL_VECTORS
   fractals.koch_snowflake.VECTOR_1
   fractals.koch_snowflake.VECTOR_2
   fractals.koch_snowflake.VECTOR_3
   fractals.koch_snowflake.processed_vectors


Functions
---------

.. autoapisummary::

   fractals.koch_snowflake.iterate
   fractals.koch_snowflake.iteration_step
   fractals.koch_snowflake.plot
   fractals.koch_snowflake.rotate


Module Contents
---------------

.. py:function:: iterate(initial_vectors: list[numpy.ndarray], steps: int) -> list[numpy.ndarray]

   Go through the number of iterations determined by the argument "steps".
   Be careful with high values (above 5) since the time to calculate increases
   exponentially.
   >>> iterate([np.array([0, 0]), np.array([1, 0])], 1)
   [array([0, 0]), array([0.33333333, 0.        ]), array([0.5       , 0.28867513]), array([0.66666667, 0.        ]), array([1, 0])]


.. py:function:: iteration_step(vectors: list[numpy.ndarray]) -> list[numpy.ndarray]

   Loops through each pair of adjacent vectors. Each line between two adjacent
   vectors is divided into 4 segments by adding 3 additional vectors in-between
   the original two vectors. The vector in the middle is constructed through a
   60 degree rotation so it is bent outwards.
   >>> iteration_step([np.array([0, 0]), np.array([1, 0])])
   [array([0, 0]), array([0.33333333, 0.        ]), array([0.5       , 0.28867513]), array([0.66666667, 0.        ]), array([1, 0])]


.. py:function:: plot(vectors: list[numpy.ndarray]) -> None

   Utility function to plot the vectors using matplotlib.pyplot
   No doctest was implemented since this function does not have a return value


.. py:function:: rotate(vector: numpy.ndarray, angle_in_degrees: float) -> numpy.ndarray

   Standard rotation of a 2D vector with a rotation matrix
   (see https://en.wikipedia.org/wiki/Rotation_matrix )
   >>> rotate(np.array([1, 0]), 60)
   array([0.5      , 0.8660254])
   >>> rotate(np.array([1, 0]), 90)
   array([6.123234e-17, 1.000000e+00])


.. py:data:: INITIAL_VECTORS

.. py:data:: VECTOR_1

.. py:data:: VECTOR_2

.. py:data:: VECTOR_3

.. py:data:: processed_vectors