Image:ExtremeValueTheorem.png

From Wikipedia, the free encyclopedia

[edit] Summary

A continuous function on a closed interval, showing the extreme value theorem.

I generated the function with the Python script:

#!/usr/bin/python
from random import *
 
k = 0
for i in xrange(1000000):
    k += gauss(0, 1)
    print i, k

I redirected the output to a file, then I plotted it with gnuplot with:

set term png size 6000,4500
set out 'out.png'
pl [][-600:700] 'randfunc.txt' w p ps 3 pt 7

ps 3 pt 7 gives circular dots of 17 pixels in diameter. The high number of samples caused them to overlap, forming a continuous line. (Actually, in the places where the function happened to change very quickly, there were gaps between them, but in the downscaled version they are not evident.) Then I used GIMP to change the color of the graph, add a blue and a green dot at the bottom and the top, Gaussian blur it at 2 pixels, and downscale it to its current size with cubic interpolation.

[edit] Licensing


I, the copyright holder of this work, hereby publish it under the following licenses:
GFDL Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. Subject to disclaimers.
Creative Commons: Some Rights Reserved
BYSA		 This file is licensed under the Creative Commons Attribution-ShareAlike license versions 2.5, 2.0, and 1.0.
You may select the license of your choice.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current13:50, 22 January 20081,300×975 (123 KB)Army1987 (Talk | contribs) (A continuous function.)
23:54, 21 January 20081,300×975 (154 KB)Army1987 (Talk | contribs) (A continuous function, showing the extreme value theorem. The maximum is shown in green and the minimum in blue. I generated it with this Python script: <source lang="Python"> #!/usr/bin/python from random import * k = 0 for i in range(100000): k += )
20:18, 21 January 2007300×150 (9 KB)Army1987 (Talk | contribs) (A continuous function on a closed interval, showing the extreme value theorem. The function is the integral of a piecewise continuous function which, on each one of 256 very small interval, takes a normally distributed randomly choosen value. I p)

The following pages on the English Wikipedia link to this file (pages on other projects are not listed):