本文共 19057 字，大约阅读时间需要 63 分钟。

复杂现象背后的推动力，可能是极其简单的原理。科学的目标之一就是发现纷繁复杂的自然现象背后的简单法则。爱因斯坦的相对论是这方面的典范例证。     很早的时候，生物学家观察某区域某种昆虫的数量（称为虫口数）之逐年变化规律，就十分迷惑：有的时候是逐渐增多达到一个平衡值。有的时候在两个数字间周期跳动。有的时候则进入一片混乱，类似随机数字一样变化（称为混沌现象）。     慢慢地，人们从数学中更清晰地观察到了这一现象，并因此开创了：符号动力学、非线性动力学等研究领域。     一个著名的虫口数目简化模型如下：     x' = x * (1 - x) * r     这里，x  x' r 都是浮点数。       其中，x 表示当年的虫口数，x' 表示下一年的虫口数。它们的取值范围在 0 与 1 之间，实际上表示的是：虫口的总数占环境所能支持的最大数量的比率。     r 是常数（环境参数），r的取值范围在 [0,4]。     令人惊讶的是：这个简单的迭代公式有着不同寻常的神秘性质！     一般来说，多次迭代后，虫口数的稳定模式与x的初始值无关，而与 r 有关！     例如：无论x初始值是多少，当 r = 2.5 的时候，x 多次迭代后会趋向于 0.6。     而当 r = 3.2 的时候，x 的值会趋向于在 0.799 与 0.513 之间周期性摆动。     那么，r = 3.62 的时候，你观察到有什么周期现象发生吗？     不需要提交源代码，只要写出你的结论即可！

    答案写在：“解答.txt”中，不要写在这里。

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很多人可能会想到递归 但这个题用for更简单一点 

public class 数量周期 {	public static void main(String[] args) {		double x = 0.5;		double y = 0;		double r = 3.62;	//改变这个就行了				for (int i = 0; i != 999; ++i) {			y = x * (1 - x) * r;			x = y;			System.out.println(y);		}	}}

本来以为结果可能是一个固定常数 后来才发现这个题还得分析一下 我们输出999个数据看下

0.9050.311229499999999940.77600382795369490.62923523077676390.84453968355639720.475278511366584830.90278762975908760.31769889363326350.78469402995521910.61159649969444170.85991732094653340.43606346993926570.89020187484813010.353827838651315340.82765399127288770.5163671604506660.90403026013279140.314069567007244640.77985614419539810.62148354957302610.851575124802960.457549652463614730.89847664413842530.33020323795576710.80063199574944480.57782585933677510.88307415093894280.37378018547431720.847328181484390.468294546335222770.90136104643263660.321851703671526160.79011272794524940.60032127040467980.86856702658989590.41325321581667230.87775948347054130.388417936986012740.8599289844330240.436033076717343260.89018780246721760.35386759327700890.82769605733335360.51626736430959510.90404204974747650.314035079769805050.77980971536647360.62157761393524960.85149235931911730.45776029925181560.89854122380414790.33001691240186530.80040281474878970.57832449898543570.88279228774842330.374561633273988340.84804008247426050.46650252558854190.90093806753315450.32308017093006220.79169173417634780.59699567461176550.87094245756592280.406894129293331850.87361929456063050.399679214289900940.86856737863532040.41325227640931590.87775889347564020.3884195506082170.85993028799497040.43602967977756480.89018622923291360.35387203759154080.8277007593405140.51625620862609490.90404336316559970.31403123766822920.77980454236117740.62158809342806860.85148313464222860.45778377394470430.89854840073268630.32999620362977360.80037732737535240.57837992953980210.88276084365611510.374648774360445750.84811919423499480.46630315631074420.90088957226588230.323220934071490160.79187196589498570.59661493499903870.87120930669317610.406177215260224930.87313417193049910.400990620850621370.86951365708244570.410723959170995470.87614783449271050.3928163599153290.8634122356194830.426912200147418760.88566258811600660.36657701262214160.84055786930978760.485153622297263050.90420209795016980.31356680372590640.77917844124383160.62285502055968530.8503620510022710.460632088247284970.89938960643771420.327566351015690650.79736522484660070.5848976014479890.878908478111530.38527068207903930.8573506046659960.44272797414834630.8931260924985480.34553578893649950.818629723151920.53747986027735370.8999148414663960.326046592861164660.7954595679641420.58898719018836210.87633423353621660.392308611700724230.86301728488795230.42795079215873710.88620826017099640.36505231078800490.83907661865836090.48879790897874920.90454573762744080.312560741126240660.77781681772293810.62560049316088530.84789274834622760.46687370104615220.90102758690978550.32282028582507840.7913586029633130.5976987954149450.87044690225557690.40822411524547450.87450941685863710.397268561996816870.86679543095778930.417969224819132350.88064084596207790.380507417914690670.85331191263223990.45311790645957740.89704349088506690.33433040817179540.80564398256338340.56682595644051490.88883413539583370.35768501484652770.83168213090277640.50675280982405250.90483492640531830.311713430151889960.77666436676569460.62791371794693670.84576985235478930.47220441731322090.90220320821083070.3194019370837930.78693130960870770.60696693330975950.86358023214546580.42647008155083820.88542793095615190.36723202234067250.84118904407187340.483595931063262760.90402588161079410.31408237489880650.77987338476977010.62144861636099420.85160584557408010.457471452276452750.89845258791526420.330272637364735830.80071729298981680.57764017710269370.88317865049605380.37349032093056340.84706298998832840.468961157148908460.90151245664876410.321411644704265030.7895444416570070.60151373902602610.86769575805602030.415575382817543140.87919839212921610.38447505745195440.85668743529036020.444442146091666160.8938262360261430.34354124285928020.81638477947661230.54264043016223830.8984180932503970.3303721431539990.8008395324582340.57737398407132630.88332802505192710.373075843259436770.8466827355372230.469916112787149070.90172375422319540.320797251560014540.78874867732463020.60317960886266130.86646136530011260.41885596522740620.88116463714738320.37906294018565930.85205470377973450.456328097678559640.89809580911040820.33130141090280060.80197764545254370.57489039596191490.88469697150545680.36926982921459780.84313283325603890.478780688644893870.90337006178872660.31599918757426320.78244019771654130.61622367566410470.85610124711875250.44595468451769850.8944263560253950.34182881581455260.81443439290601130.54709426545933780.89697131118226040.334537876715617970.80589267444477080.56627541163011230.88909940272399820.356937990375376770.83091040627583450.50860385692647110.90473202459847960.3120149975171850.77707513260636040.62709032262602750.84652994061922040.47029954092107130.90180673548441330.32055587729607870.78843530071381260.60383437983371960.86597068606365960.42015695413038150.88192281865506840.37696855733785520.85020501610162650.461030337044079530.8995025426361490.327239740706651960.79695709196820050.58577567761783870.87836596992770620.38675787793841140.85857792288337760.439547181058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规律就是每组数据都较前一年增一次减一次

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