Quick and dirty script to generate Chladni patterns from a square plate, inspired from https://twitter.com/mcnees/status/978996740438315008

chladni.py

def chladni(n, m, N=100):
    x = np.linspace(-1,1,N)
    y = np.linspace(-1,1,N)
    xx, yy = np.meshgrid(x, y)
    sgn = -1 if n>m else 1
    return np.cos(n*np.pi*xx/2.)*np.cos(m*np.pi*yy/2.) + sgn*np.cos(m*np.pi*xx/2.)*np.cos(n*np.pi*yy/2.)

def all_chladni(nr=10, mr=10):
    fig, ax = plt.subplots(nr, mr, figsize=(nr+2.5,mr+2.5), sharex=True, sharey=True)
    for n in range(nr):
        for m in range(mr): 
            plate =  chladni(n,m,N=100)
            ax[n,m].set_aspect('equal')
            ax[n,m].set_title(r'$n=%d,\ m=%d$'%(n,m), fontsize=10)
            ax[n,m].tick_params(axis='both', which='both', bottom='off', top='off', labelbottom='off', right='off', left='off', labelleft='off')
            if plate.min() <= 0 <= plate.max():
                ax[n,m].contour(plate, 0, extent=(-1, 1, -1, 1), color='k')
    ax[0,0].set_xlim(-1.,1.)
    ax[0,0].set_ylim(-1.,1.)
    fig.suptitle(r'$\cos\left(\frac{n\pi x}{L}\right) \cos\left(\frac{m\pi y}{L}\right) \pm \cos\left(\frac{m\pi x}{L}\right)\cos\left(\frac{n\pi y}{L}\right) $', fontsize=9+np.maximum(nr,mr))
    fig.subplots_adjust(top=.88, bottom=0.08, hspace=.5, wspace=.5)
    fig.savefig('chladni_{}_{}.pdf'.format(nr, mr))
    return