But the result is usually not satisfactory for us – it has large regions of the same color.
There is a better idea than thresholding when it comes to monochromatic images:

1. Take original image:

2. Apply gaussian noise:

3. Do thresholding:

After this procedure we have an image that creates illusion that it has more than 1 bit depth. It’s so called dithering.
I’ve found this idea in “Practical signal processing” written by Mark Owen.

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1. Brute-force algorithm

fibo 0 = 0
fibo 1 = 1
fibo x = fibo (x-1) + fibo(x-2)

This algorithm is easy to code and analyse
Unfortunately, due to exponential complexity, computing even 30th element of sequence took some time.

2. Linear algorithm

fibo n = head (fibo2 n)
fibo2 0 = [0,0]
fibo2 1 = [1,0]
fibo2 n = [f1+f2,f1] where (f1:f2:r)  = fibo2 (n-1)

Algorithm can quickly compute up to 15000th element – then I have stack overflow in Hugs environment.

3. Logarithmic solution
There is formally faster solution, based on Binet formula and fast exponentiation algorithm. It fails for n larger than 75 because of arithmetics errors.

fibo x = round(if x==0 then 0 else (fibo2(x, 1, (1+sqrt(5))/2) - fibo2(x, 1, (1-sqrt(5))/2))/sqrt(5))
fibo2 (0,y,z) = y
fibo2 (x,y, z) = 
    fibo2 (div  x 2, 
	(if mod x 2 == 1 then  y*z else y),
	z*z)

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• Launch gconf-editor
• Go to apps/nautilus/preferences
• Check always_use_location_entry

2. After updating Firestarter stops displaying information about blocked connections.
In order to fix:

• Open /etc/rsyslog.d/50-default.conf
• Uncomment there:
  
#*.=info;*.=notice;*.=warn;\
# auth,authpriv.none;\
# cron,daemon.none;\
# mail,news.none -/var/log/messages


• Type sudo service rsyslog restart

3. In Gnome Unity some tray icons (like Firefox, QuickSynergy or Kadu) are not diplayed.
Type:

gsettings set com.canonical.Unity.Panel systray-whitelist "['all']"
unity --replace

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hover your mouse pointer over the line, in the middle of line where the tiny
dots are – your pointer will turn into a hand. Click on the dots and
the today pane will jump out to regular size. Now it will stay the
correct size.

Click here for more details

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function numbers = randomcov(n, covMatrix, offset)
    x=randn(n,length(covMatrix(1,:)));
    numbers = x*inv(chol(cov(x)))*chol(covMatrix);
    for i=1:length(offset)
        numbers(:,i) = offset(i)+numbers(:,i)-mean(numbers(:,i));
    end
end

Usage:
n – number of vectors to generate
covMatrix – given covariance matrix
offset – vector of means of each coordinate

Example:

>> n = 1000
 
n =
 
        1000
 
>> covMatrix = [1 0.6 0.3; 0.6 4 0.5; 0.3 0.5 9]
 
covMatrix =
 
    1.0000    0.6000    0.3000
    0.6000    4.0000    0.5000
    0.3000    0.5000    9.0000
 
>> offset=  [4, 7, 5]
 
offset =
 
     4     7     5
 
>> res = randomcov(1000, [1 0.6 0.3; 0.6 1 0.5; 0.3 0.5 9], [4, 7, 5]);
>> length(res)
 
ans =
 
        1000
 
>> res(1:10,:)
 
ans =
 
    5.4045    6.7922   13.7702
    3.2959    7.8065    4.1698
    4.4234    7.5814    8.2764
    5.1770    9.1141    7.6232
    3.0880    5.7971    6.7749
    2.8736    6.6350    7.4795
    4.1235    7.1429    4.4354
    4.2488    7.5810    2.4269
    2.7958    7.3045    8.3019
    3.7704    6.5484    7.3827
 
>> cov(res)
 
ans =
 
    1.0000    0.6000    0.3000
    0.6000    1.0000    0.5000
    0.3000    0.5000    9.0000
 
>> mean(res)
 
ans =
 
    4.0000    7.0000    5.0000

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