In the early 1970s, R. May, an ecologist at Princeton University in the United States, proposed a famous model when studying the reproductive rules of insect populations: χ[n+1]=k*χ[n]*(1-χ[n] Where χ[n] represents the number of the nth generation group. Given an initial χ[0] value and then iterating over and over, it has been found that the resulting sequence χn has many interesting phenomena with the difference in k values. When the k value is between 0 and 1, χ[n] tends to zero after a certain number of iterations. When the k value is between 1 and 3, it tends to 1/k. When the k value is greater than 3, after a certain number of iterations, χ[n] alternates between 2 values, and the value of k increases to around 3.449. The alternating change value becomes four again. Continue to increase the value of k, the number of alternating values ​​of χ[n] is rapidly doubled in the order of 4→8→16→32, and finally chaos. However, when the k value is around 3.835, after a certain number of iterations, χ[n] changes very simply between the three values, and then rapidly increases in the order of 3→6→12. Repeatedly, the surprising complexity is hidden in simple equations.
In order to reflect the infinite mystery of this complexity, the following small program written in TC2.0 uses χ[n] size to control the pronunciation frequency of PC speakers, set different k values, we can hear the sound of chaos . When you execute the following small program, the k value is equivalent to a “tuning knobâ€. When the k value is set between 1 and 3, only one tone is transmitted from the speaker, which is annoying and repeating. When the k value is slightly greater than 3, it begins to have a rhythm: so-mi-so-mi.... When the k value is increased to 3.449, it becomes so-fa-la-mi-so-fa-la-mi..., and then the k value is increased, the rhythm is more complicated, and finally becomes the music work of the modern abstract composer. But the rhythm is not infinitely complicated as the value of k increases. When the k value is increased to 3.835, the pitch becomes mi-so-TI-mi-so-TI... again, and then increasing the value of k quickly becomes more complicated. Constantly changing the value of k, listening carefully, you will hear the infinite mystery of chaos.
#include
#include
#include
Main()
{
Int fMin=20, fMax=16000; /*fMin represents the lowest frequency, fMax represents the highest frequency*/
Int fDis,i; /*fDis represents the difference between the highest frequency and the lowest frequency, i is used for cyclic counting*/
Float x=0.1,k; /*x represents the size of x[n], and its initial value is set to 0.1, ie x[0]=0.1*/
Char ch;
fDis=fMax-fMin;
Clrscr();
While(1)
{
Printf("Please input The value of k(1-4.0)"); /*Enter k value*/
Printf("If you want to quit,Please input:0"); /*if k=0 exit*/
Scanf("%f",&k);
If (k==0)
{
Break;
}
Else if((k<1)||(k>4.0))
{
Printf("The number must be: 1 conTInue; / / input is wrong, continue to enter. } For(i=1;i<100;i++) /*Remove the first 100 points*/ { x=k*x*(1-x); } For (i=1;i<100;i++) { x=k*x*(1-x); /*calculate the value of x*/ Sound(x*fDis+20); /*Use the value of x to control the pronunciation frequency of the PC speaker*/ Delay(1000); If (kbhit())//kbhit() detects if there is a button event, if there is no button, it returns 0; { Ch=getch();//Read key value Switch(ch) { Case 27: Nosound();//close the sound Return(0);//ESC exit } Break; } } Nosound();//close the sound Clrscr();//clear screen } Nosound(); Return(0); } High Frequency Power Supply Transformer EE 30 abb transformer,RM6 frequency transformer,ETD44 power transformer,EFD20 high frequency transformer IHUA INDUSTRIES CO.,LTD. , https://www.ihua-coil.com