I always like to play around with my models and see what happens next. Don’t you? Problem is that most of the time we don’t know how to do it and with what resources… Let me show you how to model a Fibonacci spiral easy.

First we will use Python. Don’t worry. Install Python or just install Anaconda and open Spider.

Once in spider paste the following code to the editor and hit play.

The result should be something like this:

There is a nice page that explains how the python script works and gives a deeper insight into the Fibonacci series:

Week 1: Fibonacci Sequence and the Golden Ratio

# chromoSpirals.py # ---------------- # Code written by Peter Derlien, University of Sheffield, March 2013 # Draws spiralling patterns of circles using the Golden Angle. # ---------------- # Import from the numpy and matplotlib packages. import numpy as np import matplotlib.pyplot as plt import matplotlib from matplotlib.collections import PatchCollection import matplotlib.patches as mpatches ox=0.5; oy=0.4 # centre of plot ndiscs=300 ndiscs=input('No. of discs (e.g. 300)? ') ndiscs=int(ndiscs) ncols=input('no. of colours (1 to 34)? ') ncols=int(ncols) offset=0.0 offset=input('offset (in radians) from golden angle? ') offset = float(offset) tau=(1+5**0.5)/2.0 # golden ratio approx = 1.618033989 #(2-tau)*2*np.pi is golden angle = c. 2.39996323 radians, or c. 137.5 degrees inc = (2-tau)*2*np.pi + offset theta=0 k=0.1 # scale factor drad=k*(1+5**0.5)/4.0 # radius of each disc minv=maxv=0 # minv and maxv will be used later to display inputs chosen # now collect in list 'patches' the locations of all the discs patches = [] for j in range(1,ndiscs+1): r = k*j**0.5 theta += inc x = ox + r*np.cos(theta) y = oy + r*np.sin(theta) if y > maxv: maxv=y elif y < minv: minv=y disc = mpatches.Circle((x,y),drad) patches.append(disc) # start building the plot fig = plt.figure() ax = plt.axes([0,0,1,1]) # create text to show which inputs the user has chosen font = "sans-serif" maxv=maxv*0.95 nd = 'ndiscs: '+ str(ndiscs) plt.text(minv, maxv, nd, ha="center",family=font, size=14) setting = 'angle offset: '+ str(offset) plt.text(minv, minv, setting, ha="center",family=font, size=14) nc = 'ncols: '+ str(ncols) plt.text(maxv, maxv, nc, ha="left",family=font, size=14) # build colour cycle, using a number between 0 and 100 for each colour colcycle=[] s=100/ncols for j in range(ndiscs): colcycle.append((j%ncols)*s) # bring together the information for locations and colours of discs collection = PatchCollection(patches, cmap=matplotlib.cm.jet, alpha=1.0) collection.set_array(np.array(colcycle)) ax.add_collection(collection) ax.set_xticks([]); ax.set_yticks([]) # suppress display of axes plt.axis('equal') plt.show() # display the plot we have built

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