SCIENCE CAPSULES

              ADVT:  SMART DOORBELL IN AMAZON     With proper keys, we can lock and unlock a safe or secret.  Consider the following two strings of the alphabet.       ABCDEF.............Z AB             ABCDEF.................ZYZ     In the second string, each letter is shifted to third place.  A corresponds to C, B to D; C to E, and so on.  Suppose, you want to send the message 'BAD' you send DCF and also send 'Three' as the key .  The receiver can decode the message by shifting the alphabets to third place in the backward direction. Hence key plays key-role in cryptography.      To further strengthen our secrets, we can have a double key.  One is called the public key and the other is the private key.  Using the public key, anyone can encrypt the message and sent it through public channels.  No one can decrypt the secret message ...

      Consider this equation              p(n+1)=p(n)*r*(1-p(n))     This equation is taken from population modeling.  Here p represents population and r the rate of growth.  We need not go into the origin of the equation.  Here, the important point;  p(n) is calculated from the equation and the p(n) is fed back into the equation to get the next p(n).  The output to the input feed back calculation is repeated many times(iterated).  In computer language, the equation can also be written as                  p = p*r*(1-p)   Let initial p be 0.25 and let r be fixed at 1.5.  Let us calculate p repeatedly in a spreadsheet and draw a graph between p and number of iterations.  The screen shot is shown below.  The p initially increases and then stabilizes at 0.333.      Now let us change only r to 2.5.  As...

        Draw a triangle.  Within that, draw  another inverted triangle.  Now we get 3 triangles in 3 corners.  Within these triangles, again draw inverted triangles.  Now repeat the procedure as many times as possible.  The emerging figure is called the sierpinski gasket.  This is the good example for self similarity.  The overall structure is replicated many times throughout the figure.  And it is even present at the microscopic level.      To put in nutshell; using self similarity technique and repeating infinite number of times, one can generate complex figures.      These figures does not fall in a straight line(one dimension) or occupy the entire area of the square (two dimension).  They fall somewhere in between dimension 1 and 2.  So they are said to be having fractional dimension.  Hence they are called FRACTALS .  Fractals occurs everywhere in nature. ...