Fractal life

This week's special issue of Current Biology, especially Nicholas Butterfield's article on the Neoproterozoic, got me thinking about my favorite pre-Cambrian life form, Charnia. This organism is believed to have developed according to rigidly recursive rules, and I thought it would be fun to play with a terrific Python plotting library, pyqtgraph, in this context. I started with the discussion of recursion in this book. This animate gif is the result:

I think the result is kind of pretty. The (somewhat sloppy) code that produced the images is here:

	import pyqtgraph as pg
	import numpy as np
	import pyqtgraph.exporters
	def make_tree(order, theta, sz, basePosition, heading, data):
	trunk_ratio = 0.55
	trunk = sz * trunk_ratio
	deltaX = trunk * np.cos(heading)
	deltaY = trunk * np.sin(heading)
	newpos = (basePosition[0] + deltaX, basePosition[1] + deltaY)
	data[0].extend([basePosition[0], newpos[0], np.nan])
	data[1].extend([basePosition[1], newpos[1], np.nan])
	if order > 0:
	newsz = sz*(1 - trunk_ratio)
	make_tree(order-1, theta, newsz+newsz*np.mod(order+1,2), newpos, heading-theta, data)
	make_tree(order-1, theta, newsz+newsz*np.mod(order,2), newpos, heading+theta, data)
	return data
	win = pg.GraphicsWindow()
	win.setWindowTitle('fractal')
	win.setGeometry(100,100,800,900)
	plot = win.addPlot()
	plot.setYRange(0, 45)
	plot.setXRange(-15, 13)
	plot.hideAxis('left')
	plot.hideAxis('bottom')
	order = 0
	curves = []
	def update():
	global order, timer, curves
	if order >= 15 or order <=-1 :
	timer.stop()
	data = make_tree(order, .4, 10., (0,0), np.pi/2+.4/2, [[],[]])
	curves.append(plot.plot())
	curves[-1].setZValue(16-order)
	curves[-1].setPen(7-order/2, 7)
	curves[-1].setData(data[0], data[1], connect="finite")
	order += 2
	exporter = pg.exporters.ImageExporter(plot)
	exporter.export('fractal'+str(order)+'.png')
	timer = pg.QtCore.QTimer()
	timer.timeout.connect(update)
	timer.start(1000)

view raw fractal.py hosted with ❤ by GitHub