Listen to the voice of chaos

The early 70s of this century, Princeton University ecologist R 路 May the law in the breeding of insect groups, made a famous model: 蠂 [n +1] = k * 蠂 [n] * (1-蠂 [n ])


Where 蠂 [n] n behalf of the group, said the first number. When given an initial 蠂 [0] value, and then kept iteration, it was found with different k values to obtain the sequence 蠂n There are many interesting phenomena. When the k value is between 0 and 1 when, 蠂 [n] after a certain number of iterations have tended to 0. When the k value is between 1 and 3 hours tend to 1 / k, when k is greater than 3, after a certain number of iterative 蠂 [n] alternate between the two values change, k value increased to 3.449 near the change in value has become the turn 4. Continue to increase the k value, 蠂 [n] the number of alternate values by 4 鈫?8 鈫?16 鈫?32 in the order of the rapid doubling, and finally a chaos. But when the k value of 3.835 near, after a certain number of iterations, 蠂 [n] is simply alternating between the three values change rapidly followed by 3 鈫?6 鈫?12 of the order of rapid growth. So repeatedly, in a simple equation hides surprising complexity. 蠂 [n] with k changes as shown below:

To reflect this complex into the infinite mystery, the following small programs written using TC2.0 with 蠂 [n] size to control the PC speaker sound frequency, set different k values, we can listen to the voice of Chaos .
# Include
# Include
銆??main(){
銆??int fMin=20,fMax=16000; /锛奻Min浠ｈ〃鏈?綆棰戠巼锛宖Max浠ｈ〃鏈?珮棰戠巼锛?
銆??int fDis,i,j; /锛奻Dis浠ｈ〃鏈?珮棰戠巼鍜屾渶浣庨鐜囦箣闂寸殑宸?锛?
銆??/锛奿,j鐢ㄤ簬寰幆璁版暟锛?
銆??float x=0.1,k; /锛妜浠ｈ〃x[n]鐨勫ぇ灏忥紝璁惧畾鍏跺垵濮嬪?涓?.1锛屽嵆x[0]=0.1锛?
銆??fDis=fMax锛峟Min;
銆??for(j=1;;j锛嬶紜){
銆??printf("Please input The value of k(1锛?.0)n"); /锛婅緭鍏鍊硷紛/
銆??printf("If you want to quit,Please input:0n"); /锛婂鏋渒=0閫?嚭锛?
銆??scanf("锛協",锛唊);
銆??if (k==0) break;
銆??for(i=1;i<100;i锛嬶紜) /锛婂幓闄ゅ紑濮嬬殑100涓偣锛?
銆??x=k锛妜锛?1锛峹);
銆??for (i=1;i<100;i锛嬶紜){
銆??x=k锛妜锛?1锛峹); /锛婅绠梮鐨勫?锛?
銆??sound(x锛奻Dis锛?0); /锛婄敤x鐨勫?鎺у埗PC鍠囧彮鐨勫彂闊抽鐜囷紛/
銆??delay(1000); }
銆??nosound(); }}
銆??鎵ц涓婇潰鐨勫皬绋嬪簭鏃讹紝k鍊煎氨鐩稿綋浜庝竴涓?璋冮煶鏃嬮挳鈥濄?褰撳皢k鍊艰瀹氬湪1涓?涔嬮棿鏃讹紝鍠囧彮閲屼紶鍑虹殑鍙湁涓?釜闊宠皟锛岄噸澶嶅張鐑︿汉銆傚綋k鍊肩◢绋嶅ぇ浜?鏃讹紝渚垮紑濮嬫湁浜嗛煹寰嬶細so锛峬i锛峴o锛峬i鈥︺?k鍊煎鍔犲埌3.449鏃讹紝鍙樻垚浜唖o锛峟a锛峫a锛峬i锛峴o锛峟a锛峫a锛峬i鈥︼紝鍐嶅鍔爇鍊硷紝闊靛緥鏇村姞澶嶆潅锛岀粓浜庢垚浜嗙幇浠ｆ娊璞℃淳浣滄洸瀹剁殑闊充箰浣滃搧銆備絾鏄煹寰嬪苟涓嶆槸闅忕潃k鍊肩殑澧炲姞鏃犻檺鍦板鏉備笅鍘汇?鍦╧鍊煎鍔犲埌3.835鏃讹紝闊宠皟鍙堝彉鎴愪簡mi锛峴o锛峵i锛峬i锛峴o锛峵i鈥︼紝鍐嶅鍔爇鍊煎張杩呴?鍦板彉寰楁洿鍔犲鏉傘?
涓嶅仠鍦版敼鍙榢鍊硷紝浠旂粏鑱嗗惉锛屼細鍚埌娣锋矊涓殑鏃犻檺濂ュ銆?br />





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