Bernstein polynomials based coloring

In [102]:

    

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors as col
import matplotlib.cm as cm


    

In [103]:

    

def rgb_continuous_bernstein(escape_time, bailout, rgb_base, rgb_amp):
    '''
    Convert cont_index with rgb_base rgb_freq and rgb_phase to a rgb value between 0 and 255 
    using adapted Bernstein polynomial
    '''
    red = rgb_base[0]
    green = rgb_base[1]
    blue = rgb_base[2]
    if (escape_time == bailout):
        return (0, 0, 0)
    
    index_mapped = escape_time / bailout
    
    if (rgb_amp[0] > 0):
        red = np.abs(rgb_amp[0] * (1 - index_mapped) * np.power(index_mapped, 3) * (255 - rgb_base[0]) + rgb_base[0] )
    if (rgb_amp[1] > 0):
        green = np.abs(rgb_amp[1] * np.power((1 - index_mapped), 2) * np.power(index_mapped, 2 ) * (255 - rgb_base[1]) + rgb_base[1])
    if (rgb_amp[2] > 0):
        blue = np.abs(rgb_amp[2] * np.power((1 - index_mapped), 3) * index_mapped * (255 - rgb_base[2]) + rgb_base[2])
    
    rgb = np.array([red, green, blue])
    return rgb.astype(int)


    

In [104]:

    

def generate_rgb_tuples(escape_idx, bailout, rgb_base, rgb_amp):
    '''
    Fill arrays with rgb tuples
    '''
    rgb_tuples = np.zeros((escape_idx.size,3), dtype='uint8')
    tuples_idx = 0
    
    for etime in escape_idx:
        rgb_tuples[tuples_idx] = rgb_continuous_bernstein(etime,
                                                bailout,
                                                rgb_base,
                                                rgb_amp)
        # print(rgb_tuples[tuples_idx])
        tuples_idx +=1
        
    return rgb_tuples


    

In [105]:

    

escape_idx = np.linspace(0, 1000, 1001)
rgb_tuples_1 = generate_rgb_tuples(escape_idx, 
                                   escape_idx.size,
                                   (0, 0, 0),
                                   # you have to adjust the frequency so it corresponds with the fractal bailout
                                   (9, 15, 8.5))


    

In [106]:

    

bounds = np.arange(0, 1000, 1)
norm_obj_1 = col.Normalize(vmin=0,
                           vmax=255)


    

In [107]:

    

colmap_1 = col.ListedColormap(norm_obj_1(rgb_tuples_1))
print(colmap_1)


    

    




<matplotlib.colors.ListedColormap object at 0x7f03e467acc0>

In [108]:

    

norm_1 = mpl.colors.BoundaryNorm(bounds, colmap_1.N)


    

In [109]:

    

fig = plt.figure(1, figsize=(10, 6))
fig.suptitle("Modified Bernstein polynomials", fontsize='medium', weight='bold')
ax_1 = fig.add_subplot(111)
ax_1.plot(escape_idx, rgb_tuples_1.T[0], c='red', lw=2)
ax_1.plot(escape_idx, rgb_tuples_1.T[1], c='green', lw=2)
ax_1.plot(escape_idx, rgb_tuples_1.T[2], c='blue', lw=2)
ax_1.set_xlabel("Continuous Index")
ax_1.set_ylabel("Color Channel")
rgb_settings_1 = "rgb-base=0,0,0 rgb-amp=9,15,8.5"
ax_1.text(0.5, 0.92, rgb_settings_1,
         horizontalalignment='center',
         fontsize='small',
          weight='bold',
         transform = ax_1.transAxes)
ax_1.grid()
# make room for an additional axis at the bottom
fig.subplots_adjust(top=0.93, bottom=0.27)
# get the bounding box
box = ax_1.get_position()
# use the box to position the colorbar
ax_colb = fig.add_axes([box.x0, box.y0 - 0.18, box.width, 0.1])
cb_1 = mpl.colorbar.ColorbarBase(ax_colb, cmap=colmap_1,
                                 norm=norm_1,
                                 boundaries=bounds,
                                 # extend='both',
                                 # Make the length of each extension
                                 # the same as the length of the
                                 # interior colors:
                                 extendfrac='auto',
                                 spacing='uniform',
                                 orientation='horizontal')
cb_1.set_label("Color spectrum from black to black")


    

In [110]:

    

plt.show()


    

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