import holoviews as hv
from holoviews import opts
import numpy as np
hv.extension('bokeh')

def clifford_equation(a,b,c,d,x0,y0):
    xn,yn = x0,y0
    coords = [(x0,y0)]
    for i in range(10000):
        x_n1 = np.sin(a*yn) + c*np.cos(a*xn)
        y_n1 = np.sin(b*xn) + d*np.cos(b*yn)
        xn,yn = x_n1,y_n1
        coords.append((xn,yn))
    return coords

opts.defaults(
    opts.Curve(color='black'),
    opts.Points(color='red', alpha=0.1, width=400, height=400))

def clifford_attractor(a,b,c,d):
    return hv.Points(clifford_equation(a,b,c,d,x0=0,y0=0))

clifford_attractor(a =-1.5, b=1.5, c=1, d=0.75 )

clifford = hv.DynamicMap(clifford_attractor, kdims=['a','b','c','d'])
clifford

# When run live, this cell's output should match the behavior of the GIF below
clifford.redim.range(a=(-1.5,-1),b=(1.5,2),c=(1,1.2),d=(0.75,0.8), x=(-2,2), y=(-2,2))

def interactive_clifford(a,b,c,d,x=0,y=0):
    coords = clifford_equation(a,b,c,d,x0=x,y0=y)
    
    points = hv.Points(coords).opts(color='green')
    start  = hv.Points(coords[0]).opts(color='black', size=10, alpha=1)
    step   = hv.Curve(coords[:2], group='Init')
    text   = hv.Text(0,1.75, 'x:{x:.2f} y:{y:.2f}'.format(x=coords[0][0],y=coords[0][1]))
    
    return points * start * step * text

from holoviews.streams import PointerXY

# When run live, this cell's output should match the behavior of the GIF below
iclifford = hv.DynamicMap(interactive_clifford, kdims=['a','b','c','d'], streams=[PointerXY(x=0,y=0)])
iclifford.redim.range(a=(-1.4,-1),b=(1.6,1.8),c=(1,1.5),d=(0.7,0.8), x=(-2,2), y=(-2,2))