Recamán’s sequence - Logo of SmartOncology¶

https://en.wikipedia.org/wiki/Recamán’s_sequence

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as mclr


nt = 101                       # length of the series
nc = nt-1
a = np.zeros(nt)

#////////// generate the Recaman series ////////////////
for j in range(1,nt):
    an = a[j-1] - j 
    if (an > 0) and (not an in a): a[j] = an
    else: a[j] =  a[j-1] + j

#////////// grafics //////////////////////////////////
da = np.diff(a)
xc = a[0:-1] + 0.5*da                # center of the circles

ng = 700                             # resolution of the circles
xi = np.linspace(-1,1,ng)

def draw_circle(jn,ax,ay,r):
    x = xi*r
    y = np.sqrt(r**2 - x**2)*(-1)**jn
    return ax+x, ay+y

with plt.style.context('fast'):   # 'dark_background'
    cmap = plt.cm.get_cmap('plasma')
    cmap = plt.cm.get_cmap('hsv')
    cmap = plt.cm.get_cmap('gnuplot')
    #cmap = plt.cm.get_cmap('jet')
    #cmap = plt.cm.get_cmap('gist_rainbow')
    cmap = plt.cm.get_cmap('Blues')
    cmap = plt.cm.get_cmap('brg')
    
    fig, ax = plt.subplots(figsize=(25,12))
    for jn in range(nc):
        xg,yg = draw_circle(jn,xc[jn],0,abs(0.5*da[jn]))
        color = cmap((nc-jn)/nc)
        #color = np.array([47, 49, 147])/255.
        plt.plot(xg,yg, lw=3, color=color,alpha=1)
    plt.axis('equal');plt.axis('off');
    #plt.savefig("Reca_circles_white_50.png")
    plt.show()

with plt.style.context('dark_background'):
    fig, ax = plt.subplots(figsize=(25,12))
    plt.plot(np.arange(nt), a)
    #plt.yscale('log'); #plt.xscale('log'):
    plt.axis('off'); plt.show()