import matplotlib.pyplot as plt
from numpy import sign, empty

def make_plot(x, y, a, b, c, filename, N=20000):
	xs = empty(N)
	ys = empty(N)
	for n in range(N):
		x, y = y - sign(x)*abs(b*x - c)**0.5, a - x
		xs[n] = x
		ys[n] = y
	plt.scatter(xs, ys, c='k', marker='.', s = 1, alpha=0.5)
	plt.axes().set_aspect(1)
	plt.axis('off')
	plt.show()
	#plt.savefig(filename)
	plt.close()

make_plot(5, 5, 30.5, 2.5, 2.5, "doiley1.png")
make_plot(5, 6, 30, 3, 3, "doiley2.png")
make_plot(3, 4, 5, 6, 7, "doiley3.png")