{"id":2162,"date":"2024-05-04T22:07:32","date_gmt":"2024-05-05T05:07:32","guid":{"rendered":"https:\/\/gantovnik.com\/bio-tips\/?p=2162"},"modified":"2024-05-04T22:07:32","modified_gmt":"2024-05-05T05:07:32","slug":"422-barnsleys-fern-using-imshow","status":"publish","type":"post","link":"https:\/\/gantovnik.com\/bio-tips\/2024\/05\/422-barnsleys-fern-using-imshow\/","title":{"rendered":"#422 Barnsley\u2019s fern using imshow"},"content":{"rendered":"

\"\"<\/a><\/p>\n

The Axes method ax.imshow displays an image on the axes. In its basic usage, it takes a two-dimensional array and maps its values to the pixels on an image according to some interpolation scheme and normalization. In this case, im is a three-dimensional array of shape (n, m, 3) in which the \u201cdepth\u201d coordinate corresponds to the red, green and blue components of each pixel in the n-by-m image.<\/p>\n

\r\nimport numpy as np\r\nimport matplotlib.pyplot as plt\r\nimport matplotlib.cm as cm\r\nf1 = lambda x, y: (0., 0.16*y)\r\nf2 = lambda x, y: (0.85*x + 0.04*y, -0.04*x + 0.85*y + 1.6)\r\nf3 = lambda x, y: (0.2*x - 0.26*y, 0.23*x + 0.22*y + 1.6)\r\nf4 = lambda x, y: (-0.15*x + 0.28*y, 0.26*x + 0.24*y + 0.44)\r\nfs = [f1, f2, f3, f4]\r\nnpts = 50000\r\n# Canvas size (pixels).\r\nwidth, height = 300, 300\r\naimg = np.zeros((width, height))\r\nx, y = 0, 0\r\nfor i in range(npts):\r\n    # Pick a random transformation and apply it.\r\n    f = np.random.choice(fs, p=[0.01, 0.85, 0.07, 0.07])\r\n    x, y = f(x, y)\r\n    # Map (x, y) to pixel coordinates.\r\n    # NB we "know" that -2.2 < x < 2.7 and 0 <= y < 10.\r\n    ix, iy = int(width \/ 2 + x * width \/ 10), int(y * height \/ 12)\r\n    # Set this point of the array to 1 to mark a point in the fern.\r\n    aimg[iy, ix] = 1\r\nplt.imshow(aimg[::-1,:], cmap=cm.Greens)\r\nplt.savefig('ex422.png', dpi=100)\r\nplt.show()\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
The Axes method ax.imshow displays an image on the axes. In its basic usage, it takes a two-dimensional array and maps its values to the pixels on an image according to some interpolation scheme and normalization. In this case, im is a three-dimensional array of shape (n, m, 3) in which the \u201cdepth\u201d coordinate corresponds […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","_lmt_disableupdate":"yes","_lmt_disable":"","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[69,91,2],"tags":[],"class_list":["post-2162","post","type-post","status-publish","format-standard","hentry","category-matplotlib","category-plot","category-python"],"modified_by":"gantovnik","jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8bH0k-yS","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":93,"url":"https:\/\/gantovnik.com\/bio-tips\/2018\/12\/plots-of-nonlinear-functions\/","url_meta":{"origin":2162,"position":0},"title":"Plots of nonlinear functions","author":"gantovnik","date":"2018-12-31","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np os.chdir('\/home\/vg\/Downloads\/projects\/ex15') os.getcwd() #define model parameters x=np.linspace(-2,2,1000) #examples of nonlinear functions f1=x**2-x-1 f2=x**3-3*np.sin(x) f3=np.exp(x)-2 f4=1-x**2+np.sin(50\/(1+x**2)) fig,axes=plt.subplots(1,4,figsize=(12,3),sharey=True) for n,f in enumerate([f1,f2,f3,f4]): axes[n].plot(x,f,lw=1.5) axes[n].axhline(0,ls=':',color='k') axes[n].set_ylim(-5,5) axes[n].set_xticks([-2,-1,0,1,2]) axes[n].set_xlabel(r'$x$',fontsize=18) axes[0].set_ylabel(r'$f(x)$',fontsize=18) titles=[r'$f(x)=x^2-x-1$',r'$f(x)=x^3-3\\sin(x)$',r'$f(x)=\\exp(x)-2$', r'$f(x)=\\sin\\left(50\/(1+x^2)\\right)+1-x^2$'] for n,title in enumerate(titles): axes[n].set_title(title) plt.savefig(\"example15.png\", dpi=100) plt.show() plt.close()","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example15","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example15.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example15.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2018\/12\/example15.png?resize=525%2C300 1.5x"},"classes":[]},{"id":124,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/polynomial-fit\/","url_meta":{"origin":2162,"position":1},"title":"Polynomial fit","author":"gantovnik","date":"2019-01-03","format":false,"excerpt":"import os import matplotlib.pyplot as plt import numpy as np from numpy import polynomial as P os.chdir(r'D:\\data\\scripts\\web1\\ex24') os.getcwd() x = np.array([1, 2, 3, 4]) y = np.array([1, 3, 5, 4]) f1 = P.Polynomial.fit(x, y, 1) f2 = P.Polynomial.fit(x, y, 2) f3 = P.Polynomial.fit(x, y, 3) xx = np.linspace(x.min(), x.max(), 100)\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"example24","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example24.png?resize=525%2C300 1.5x"},"classes":[]},{"id":1718,"url":"https:\/\/gantovnik.com\/bio-tips\/2022\/12\/204-mandelbrot-fractal-using-python-2-2-2-2-2-2\/","url_meta":{"origin":2162,"position":2},"title":"#325 Finding the intersection points between two functions using python","author":"gantovnik","date":"2022-12-13","format":false,"excerpt":"[code language=\"python\"] from scipy.optimize import fsolve import numpy as np import matplotlib.pyplot as plt # Defining function to simplify intersection solution def findIntersection(func1, func2, x0): return fsolve(lambda x : func1(x) - func2(x), x0) # Defining functions that will intersect funky = lambda x : np.cos(x \/ 5) * np.sin(x \/\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2022\/12\/ex325.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2022\/12\/ex325.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2022\/12\/ex325.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":1153,"url":"https:\/\/gantovnik.com\/bio-tips\/2021\/11\/201-polyfit-and-polyval-2-2\/","url_meta":{"origin":2162,"position":3},"title":"#203 Find minimum of Rosenbrock function using scipy.optimize","author":"gantovnik","date":"2021-11-23","format":false,"excerpt":"[code language=\"python\"] import numpy as np import matplotlib.pyplot as plt import scipy.optimize as so rosenbrockfunction = lambda x,y: (1-x)**2+100*(y-x**2)**2 X,Y = np.meshgrid(np.linspace(-.5,1.5,100), np.linspace(-1.5,3.,100)) Z = rosenbrockfunction(X,Y) plt.figure(figsize=(4,3), dpi=72) cs=plt.contour(X,Y,Z,np.logspace(-0.5,3.5,20,base=10),cmap='gray',linewidths=1.0) rosen=lambda x: rosenbrockfunction(x[0],x[1]) solution, iterates = so.fmin_powell(rosen,x0=np.array([0,-0.7]),retall=True) x,y=zip(*iterates) plt.plot(x,y,'.',c=\"red\") # plot black bullets plt.plot(x,y,':',c=\"red\",linewidth=1.5) # plot black dotted lines plt.clabel(cs) plt.savefig('ex203.png')\u2026","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2021\/11\/ex203.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1738,"url":"https:\/\/gantovnik.com\/bio-tips\/2023\/01\/204-mandelbrot-fractal-using-python-2-2-2-2-2-2-2-2\/","url_meta":{"origin":2162,"position":4},"title":"#329 Golden section method using python","author":"gantovnik","date":"2023-01-03","format":false,"excerpt":"golden.py [code language=\"python\"] import math as mt def golden(f,a,b,tol=1.0e-10): # Golden section method for determining x # that minimizes the scalar function f(x). # The minimum must be bracketed in (a,b). c1 = (mt.sqrt(5.0)-1.0)\/2.0 c2 = 1.0 - c1 nIt = int(mt.ceil(mt.log(tol\/abs(a-b))\/mt.log(c1))) # first step x1 = c1*a + c2*b\u2026","rel":"","context":"In "optimization"","block_context":{"text":"optimization","link":"https:\/\/gantovnik.com\/bio-tips\/category\/optimization\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2023\/01\/ex329.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":370,"url":"https:\/\/gantovnik.com\/bio-tips\/2019\/01\/roots-of-equation\/","url_meta":{"origin":2162,"position":5},"title":"#52 Roots of equation using python","author":"gantovnik","date":"2019-01-29","format":false,"excerpt":"[code language=\"python\"] import os import numpy as np import matplotlib.pyplot as plt from scipy.optimize import brentq os.chdir(r'D:\\projects\\wordpress\\ex52') os.getcwd() f=lambda x: 0.2+x * np.cos(3\/x) x=np.linspace(-1,1,1000) plt.plot(x,f(x)) plt.axhline(0,color='k') xstar=brentq(f,-0.7,-0.5) print(xstar,f(xstar)) plt.plot(xstar,f(xstar), 'ro') plt.text(-1.0, -0.5, 'x=%6.4f and f(x)=%6.4f' % (xstar, f(xstar))) plt.tight_layout() plt.savefig(\"example52.png\", dpi=300) plt.show() plt.close() [\/code]","rel":"","context":"In "python"","block_context":{"text":"python","link":"https:\/\/gantovnik.com\/bio-tips\/category\/python\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/gantovnik.com\/bio-tips\/wp-content\/uploads\/2019\/01\/example62.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/comments?post=2162"}],"version-history":[{"count":2,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2162\/revisions"}],"predecessor-version":[{"id":2165,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/posts\/2162\/revisions\/2165"}],"wp:attachment":[{"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/media?parent=2162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/categories?post=2162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gantovnik.com\/bio-tips\/wp-json\/wp\/v2\/tags?post=2162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}