adding koch examples

Author: jposada202020

docs/examples.rst

@@ -194,6 +194,17 @@ Cartesian koch snowflake example
     :lines: 5-
 .. image:: ../docs/koch.jpg
 
+
+Cartesian Koch Curve
+---------------------------
+
+Cartesian koch curve example
+
+.. literalinclude:: ../examples/cartesian_koch_2.py
+    :caption: examples/cartesian_koch_2.py
+    :lines: 5-
+.. image:: ../docs/koch2.jpg
+
 ==================
 Bar Examples
 ==================

docs/koch2.jpg

@@ -0,0 +1,60 @@
+# SPDX-FileCopyrightText: Copyright (c) 2023 Jose D. Montoya
+#
+# SPDX-License-Identifier: MIT
+
+# Example adapted to use in CircuitPython and Microplot from
+# Heltonbiker
+# https://stackoverflow.com/questions/7409938/fractal-koch-curve
+
+import math
+import board
+from circuitpython_uplot.plot import Plot
+from circuitpython_uplot.cartesian import Cartesian
+
+angles = [math.radians(60 * x) for x in range(6)]
+sines = [math.sin(x) for x in angles]
+cosin = [math.cos(x) for x in angles]
+
+
+def L(angle, coords, jump):
+    return (angle + 1) % 6
+
+
+def R(angle, coords, jump):
+    return (angle + 4) % 6
+
+
+def F(angle, coords, jump):
+    coords.append(
+        (coords[-1][0] + jump * cosin[angle], coords[-1][1] + jump * sines[angle])
+    )
+    return angle
+
+
+decode = dict(L=L, R=R, F=F)
+
+
+def koch(steps, length=200, startPos=(0, 0)):
+    pathcodes = "F"
+    for i in range(steps):
+        pathcodes = pathcodes.replace("F", "FLFRFLF")
+
+    jump = float(length) / (3**steps)
+    coords = [startPos]
+    angle = 0
+
+    for move in pathcodes:
+        angle = decode[move](angle, coords, jump)
+
+    return coords
+
+
+TOTALWIDTH = 300
+display = board.DISPLAY
+plot = Plot(0, 0, display.width, display.height, padding=0)
+points = koch(5, TOTALWIDTH, (-TOTALWIDTH / 2, 0))
+x_coordinates, y_coordinates = zip(*points)
+
+# Adding the Cartesian plot
+Cartesian(plot, x_coordinates, y_coordinates)
+display.show(plot)