\u5b9f\u884c\u7d50\u679c
\nDepth=0 Norm=1.0093 e0=1.0093 e1=0.0000
\n\u2192 \u5e72\u6e09 Norm=1.0309 e0=1.0309 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=1 Norm=1.0308 e0=1.0302 e1=0.0000
\n\u2192 \u5e72\u6e09 Norm=1.0307 e0=1.0307 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=2 Norm=1.0244 e0=1.0162 e1=0.1077
\n\u2192 \u5e72\u6e09 Norm=0.9468 e0=0.9468 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=3 Norm=0.9498 e0=0.8883 e1=0.3196
\n\u2192 \u5e72\u6e09 Norm=0.6774 e0=0.6774 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.8027 e0=0.5329 e1=0.5868
\n\u2192 \u5e72\u6e09 Norm=0.1305 e0=0.1305 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1149 e0=0.1305 e1=1.0935
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1149 e0=0.1305 e1=-1.0935
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0178 e0=0.8219 e1=-0.5868
\n\u2192 \u5e72\u6e09 Norm=1.0939 e0=1.0939 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1405 e0=1.0939 e1=-0.2969
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1405 e0=1.0939 e1=0.2969
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=3 Norm=1.0601 e0=1.0054 e1=-0.3196
\n\u2192 \u5e72\u6e09 Norm=1.0676 e0=1.0676 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=1.0686 e0=1.0664 e1=0.0092
\n\u2192 \u5e72\u6e09 Norm=0.9481 e0=0.9481 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1475 e0=0.9481 e1=0.6383
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1475 e0=0.9481 e1=-0.6383
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0710 e0=1.0688 e1=-0.0092
\n\u2192 \u5e72\u6e09 Norm=0.9559 e0=0.9559 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1477 e0=0.9559 e1=0.6233
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1477 e0=0.9559 e1=-0.6233
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=2 Norm=1.0531 e0=1.0452 e1=-0.1077
\n\u2192 \u5e72\u6e09 Norm=1.0434 e0=1.0434 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=3 Norm=1.0309 e0=1.0241 e1=0.1132
\n\u2192 \u5e72\u6e09 Norm=0.8941 e0=0.8941 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.9000 e0=0.7897 e1=0.4296
\n\u2192 \u5e72\u6e09 Norm=0.4529 e0=0.4529 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1323 e0=0.4529 e1=1.0313
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1323 e0=0.4529 e1=-1.0313
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0878 e0=0.9985 e1=-0.4296
\n\u2192 \u5e72\u6e09 Norm=1.1489 e0=1.1489 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1506 e0=1.1489 e1=0.0235
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1506 e0=1.1489 e1=-0.0235
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=3 Norm=1.0695 e0=1.0628 e1=-0.1132
\n\u2192 \u5e72\u6e09 Norm=1.0234 e0=1.0234 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.9958 e0=0.9671 e1=0.2279
\n\u2192 \u5e72\u6e09 Norm=0.7257 e0=0.7257 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1431 e0=0.7257 e1=0.8758
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1431 e0=0.7257 e1=-0.8758
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.1055 e0=1.0797 e1=-0.2279
\n\u2192 \u5e72\u6e09 Norm=1.1013 e0=1.1013 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1529 e0=1.1013 e1=0.3331
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1529 e0=1.1013 e1=-0.3331
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=1 Norm=1.0323 e0=1.0317 e1=0.0000
\n\u2192 \u5e72\u6e09 Norm=1.0356 e0=1.0356 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=2 Norm=1.0282 e0=1.0225 e1=0.1077
\n\u2192 \u5e72\u6e09 Norm=0.9561 e0=0.9561 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=3 Norm=0.9549 e0=0.8988 e1=0.3201
\n\u2192 \u5e72\u6e09 Norm=0.6896 e0=0.6896 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.8061 e0=0.5456 e1=0.5887
\n\u2192 \u5e72\u6e09 Norm=0.1427 e0=0.1427 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1160 e0=0.1427 e1=1.0991
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1160 e0=0.1427 e1=-1.0991
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0233 e0=0.8337 e1=-0.5887
\n\u2192 \u5e72\u6e09 Norm=1.1030 e0=1.1030 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1415 e0=1.1030 e1=-0.2879
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1415 e0=1.1030 e1=0.2879
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=3 Norm=1.0636 e0=1.0135 e1=-0.3201
\n\u2192 \u5e72\u6e09 Norm=1.0720 e0=1.0720 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=1.0690 e0=1.0689 e1=0.0132
\n\u2192 \u5e72\u6e09 Norm=0.9455 e0=0.9455 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1480 e0=0.9455 e1=0.6495
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1480 e0=0.9455 e1=-0.6495
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0752 e0=1.0750 e1=-0.0132
\n\u2192 \u5e72\u6e09 Norm=0.9661 e0=0.9661 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1485 e0=0.9661 e1=0.6172
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1485 e0=0.9661 e1=-0.6172
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=2 Norm=1.0542 e0=1.0486 e1=-0.1077
\n\u2192 \u5e72\u6e09 Norm=1.0433 e0=1.0433 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=3 Norm=1.0294 e0=1.0223 e1=0.1147
\n\u2192 \u5e72\u6e09 Norm=0.8888 e0=0.8888 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.8967 e0=0.7827 e1=0.4325
\n\u2192 \u5e72\u6e09 Norm=0.4428 e0=0.4428 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1320 e0=0.4428 e1=1.0355
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1320 e0=0.4428 e1=-1.0355
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.0868 e0=0.9948 e1=-0.4325
\n\u2192 \u5e72\u6e09 Norm=1.1497 e0=1.1497 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1506 e0=1.1497 e1=0.0130
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1506 e0=1.1497 e1=-0.0130
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=3 Norm=1.0710 e0=1.0642 e1=-0.1147
\n\u2192 \u5e72\u6e09 Norm=1.0284 e0=1.0284 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=4 Norm=0.9996 e0=0.9738 e1=0.2249
\n\u2192 \u5e72\u6e09 Norm=0.7357 e0=0.7357 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1437 e0=0.7357 e1=0.8713
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1437 e0=0.7357 e1=-0.8713
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=4 Norm=1.1064 e0=1.0831 e1=-0.2249
\n\u2192 \u5e72\u6e09 Norm=1.1002 e0=1.1002 e1=0.0000
\n[\u901a\u5e38\u306e\u5b50]
\nDepth=5 Norm=1.1532 e0=1.1002 e1=0.3436
\n[\u5171\u5f79\u306e\u5b50]
\nDepth=5 Norm=1.1532 e0=1.1002 e1=-0.3436<\/p>\n
C++Builder2007 \u30bd\u30fc\u30b9\u30b3\u30fc\u30c9
\n\/\/************************
\n\/\/****\u00a0 Unit1.h ***********
\n\/\/************************<\/p>\n
\/\/—————————————————————————<\/p>\n
#ifndef Unit1H
\n#define Unit1H
\n\/\/—————————————————————————
\n#include <Classes.hpp>
\n#include <Controls.hpp>
\n#include <StdCtrls.hpp>
\n#include <Forms.hpp>
\n\/\/—————————————————————————
\nstruct Octonion {
\ndouble e[8];<\/p>\n
Octonion(double a0=0.0, double a1=0.0, double a2=0.0, double a3=0.0,
\ndouble a4=0.0, double a5=0.0, double a6=0.0, double a7=0.0);<\/p>\n
Octonion operator+(const Octonion& o) const;
\nOctonion operator*(const Octonion& o) const; \/\/ \u2190 \u5909\u66f4\uff1a\u5b8c\u5168\u4e57\u7b97
\nOctonion operator*(double scalar) const; \/\/ \u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\u306f\u6b8b\u3059
\ndouble Norm() const;<\/p>\n
Octonion Conjugate() const; \/\/ \u6a19\u6e96\u7684\u306a\u5171\u5f79
\nOctonion PhaseConjugate() const; \/\/ \u4f4d\u76f8\u5171\u5f79\u7528\uff08\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u62e1\u5f35\u53ef\u80fd\uff09
\n};<\/p>\n
class RecursiveOcto {
\npublic:
\nint depth;
\nOctonion value;
\nRecursiveOcto* child; \/\/ \u901a\u5e38\u306e\u5b50
\nRecursiveOcto* childConj; \/\/ \u5171\u5f79\u306e\u5b50\uff08\u8ffd\u52a0\uff09
\nOctonion interference; \/\/ \u5e72\u6e09\u7d50\u679c\u3092\u4fdd\u6301\u3059\u308b\u30e1\u30f3\u30d0\u30fc\u3092\u8ffd\u52a0<\/p>\n
RecursiveOcto(int d, Octonion init);
\n~RecursiveOcto();
\nvoid Generate(int maxDepth);
\nvoid Dump(TMemo* memo);
\n};<\/p>\n
class TForm1 : public TForm
\n{
\n__published: \/\/ IDE-managed Components
\nTButton *ButtonExit;
\nTButton *Button1;
\nTMemo *Memo1;
\nvoid __fastcall ButtonExitClick(TObject *Sender);
\nvoid __fastcall Button1Click(TObject *Sender);
\nprivate: \/\/ User declarations
\npublic: \/\/ User declarations
\n__fastcall TForm1(TComponent* Owner);
\n};
\n\/\/—————————————————————————
\nextern PACKAGE TForm1 *Form1;
\n\/\/—————————————————————————
\n#endif<\/p>\n
<\/p>\n
\/\/************************
\n\/\/****\u00a0 Unit1.cpp *********
\n\/\/************************<\/p>\n
\/\/—————————————————————————<\/p>\n
#include <vcl.h>
\n#pragma hdrstop<\/p>\n
#include <math.h>
\n#include “Unit1.h”
\n\/\/—————————————————————————
\n#pragma package(smart_init)
\n#pragma resource “*.dfm”
\nTForm1 *Form1;
\n\/\/—————————————————————————
\n__fastcall TForm1::TForm1(TComponent* Owner)
\n: TForm(Owner)
\n{
\n}
\n\/\/—————————————————————————
\nvoid __fastcall TForm1::ButtonExitClick(TObject *Sender)
\n{
\nClose();
\n}
\n\/\/—————————————————————————
\n\/\/—————————————————————————<\/p>\n
Octonion::Octonion(double a0, double a1, double a2, double a3,
\ndouble a4, double a5, double a6, double a7) {
\ne[0]=a0; e[1]=a1; e[2]=a2; e[3]=a3;
\ne[4]=a4; e[5]=a5; e[6]=a6; e[7]=a7;
\n}<\/p>\n
Octonion Octonion::Conjugate() const {
\nreturn Octonion(
\ne[0],
\n-e[1], -e[2], -e[3], -e[4], -e[5], -e[6], -e[7]
\n);
\n}<\/p>\n
Octonion Octonion::PhaseConjugate() const {
\nreturn Conjugate();
\n}<\/p>\n
Octonion Octonion::operator+(const Octonion& o) const {
\nOctonion res;
\nfor(int i=0; i<8; i++) res.e[i] = e[i] + o.e[i];
\nreturn res;
\n}<\/p>\n
RecursiveOcto::RecursiveOcto(int d, Octonion init)
\n: depth(d), value(init), child(NULL), childConj(NULL), interference(Octonion()) {}<\/p>\n
RecursiveOcto::~RecursiveOcto() {
\ndelete child;
\ndelete childConj;
\n}<\/p>\n
\/\/ \u30b9\u30ab\u30e9\u30fc\u4e57\u7b97\u306f\u6b8b\u3059
\nOctonion Octonion::operator*(double scalar) const {
\nOctonion res;
\nfor(int i=0; i<8; i++) res.e[i] = e[i] * scalar;
\nreturn res;
\n}<\/p>\n
\/\/ \u5b8c\u5168\u306a\u516b\u5143\u6570\u4e57\u7b97
\nOctonion Octonion::operator*(const Octonion& o) const {
\nOctonion res;<\/p>\n
\/\/ e0\uff08\u5b9f\u90e8\uff09
\nres.e[0] = e[0]*o.e[0] – e[1]*o.e[1] – e[2]*o.e[2] – e[3]*o.e[3]
\n– e[4]*o.e[4] – e[5]*o.e[5] – e[6]*o.e[6] – e[7]*o.e[7];<\/p>\n
\/\/ e1
\nres.e[1] = e[0]*o.e[1] + e[1]*o.e[0] + e[2]*o.e[3] – e[3]*o.e[2]
\n+ e[4]*o.e[5] – e[5]*o.e[4] – e[6]*o.e[7] + e[7]*o.e[6];<\/p>\n
\/\/ e2
\nres.e[2] = e[0]*o.e[2] – e[1]*o.e[3] + e[2]*o.e[0] + e[3]*o.e[1]
\n+ e[4]*o.e[6] + e[5]*o.e[7] – e[6]*o.e[4] – e[7]*o.e[5];<\/p>\n
\/\/ e3
\nres.e[3] = e[0]*o.e[3] + e[1]*o.e[2] – e[2]*o.e[1] + e[3]*o.e[0]
\n+ e[4]*o.e[7] – e[5]*o.e[6] + e[6]*o.e[5] – e[7]*o.e[4];<\/p>\n
\/\/ e4
\nres.e[4] = e[0]*o.e[4] – e[1]*o.e[5] – e[2]*o.e[6] – e[3]*o.e[7]
\n+ e[4]*o.e[0] + e[5]*o.e[1] + e[6]*o.e[2] + e[7]*o.e[3];<\/p>\n
\/\/ e5
\nres.e[5] = e[0]*o.e[5] + e[1]*o.e[4] – e[2]*o.e[7] + e[3]*o.e[6]
\n– e[4]*o.e[1] + e[5]*o.e[0] – e[6]*o.e[3] + e[7]*o.e[2];<\/p>\n
\/\/ e6
\nres.e[6] = e[0]*o.e[6] + e[1]*o.e[7] + e[2]*o.e[4] – e[3]*o.e[5]
\n– e[4]*o.e[2] + e[5]*o.e[3] + e[6]*o.e[0] – e[7]*o.e[1];<\/p>\n
\/\/ e7
\nres.e[7] = e[0]*o.e[7] – e[1]*o.e[6] + e[2]*o.e[5] + e[3]*o.e[4]
\n– e[4]*o.e[3] – e[5]*o.e[2] + e[6]*o.e[1] + e[7]*o.e[0];<\/p>\n
return res;
\n}<\/p>\n
double Octonion::Norm() const {
\ndouble sum = 0.0;
\nfor(int i=0; i<8; i++) sum += e[i]*e[i];
\nreturn sqrt(sum);
\n}<\/p>\n
void RecursiveOcto::Generate(int maxDepth) {
\nif (depth >= maxDepth) return;<\/p>\n
\/\/ \u901a\u5e38\u306e\u6b21\u30b9\u30c6\u30c3\u30d7
\nOctonion rotator(cos(depth * 0.15), sin(depth * 0.15), 0.05, 0, 0, 0, 0, 0);
\nOctonion next = value * rotator;
\nnext = next + Octonion(0.03, 0, 0, 0, 0, 0, 0, 0);<\/p>\n
\/\/ \u5171\u5f79\u7248
\nOctonion nextConj = next.PhaseConjugate();<\/p>\n
\/\/ \u5b50\u3092\u751f\u6210
\nchild = new RecursiveOcto(depth + 1, next);
\nchild->Generate(maxDepth);<\/p>\n
childConj = new RecursiveOcto(depth + 1, nextConj);
\nchildConj->Generate(maxDepth);<\/p>\n
\/\/ ===== \u5e72\u6e09\u8a08\u7b97 =====
\ninterference = (child->value + childConj->value) * 0.5;<\/p>\n
\/\/ ===== \u89aa\u3078\u306e\u30d5\u30a3\u30fc\u30c9\u30d0\u30c3\u30af\uff08\u3053\u3053\u304c\u8ffd\u52a0\uff09 =====
\n\/\/ \u5e72\u6e09\u7d50\u679c\u3092\u89aa\u306evalue\u306b\u5c11\u3057\u6df7\u305c\u308b\uff08\u30d5\u30a3\u30fc\u30c9\u30d0\u30c3\u30af\u5f37\u5ea6\u306f\u8abf\u6574\u53ef\u80fd\uff09
\ndouble feedbackStrength = 0.3; \/\/ 0.1?0.5\u304f\u3089\u3044\u3067\u8a66\u3059\u3068\u826f\u3044
\nvalue = value * (1.0 – feedbackStrength) + interference * feedbackStrength;
\n}<\/p>\n
void RecursiveOcto::Dump(TMemo* memo)
\n{
\nif (!memo) return;<\/p>\n
<\/p>\n
Octonion conj = value.PhaseConjugate();
\nmemo->Lines->Add(Format(“Depth=%d Norm=%.4f e0=%.4f e1=%.4f”,
\nARRAYOFCONST((depth, value.Norm(), value.e[0], value.e[1]))));<\/p>\n
\/\/ \u5e72\u6e09\u7d50\u679c\u3092\u8868\u793a\uff08\u5b50\u304c\u3042\u308b\u5834\u5408\uff09
\nif (child && childConj) {
\nmemo->Lines->Add(Format(” \u2192 \u5e72\u6e09 Norm=%.4f e0=%.4f e1=%.4f”,
\nARRAYOFCONST((interference.Norm(), interference.e[0], interference.e[1]))));
\n}<\/p>\n
if (child) {
\nmemo->Lines->Add(” [\u901a\u5e38\u306e\u5b50]”);
\nchild->Dump(memo);
\n}
\nif (childConj) {
\nmemo->Lines->Add(” [\u5171\u5f79\u306e\u5b50]”);
\nchildConj->Dump(memo);
\n}
\n}<\/p>\n
\/\/—————————————————————————
\n\/\/—————————————————————————<\/p>\n
void __fastcall TForm1::Button1Click(TObject *Sender)
\n{
\nRecursiveOcto* root = new RecursiveOcto(0, Octonion(1.0));
\nroot->Generate(5); \/\/ \u2190 2\u5206\u5c90\u306a\u306e\u3067\u6df1\u3055\u306f\u6d45\u3081\u306b\uff085?6\u63a8\u5968\uff09<\/p>\n
Memo1->Clear();
\nroot->Dump(Memo1);<\/p>\n
delete root;
\n}
\n\/\/—————————————————————————<\/p>\n","protected":false},"excerpt":{"rendered":"
\u5b9f\u884c\u7d50\u679c Depth=0 Norm=1.0093 e0=1.0093 e1=0. … \u7d9a\u304d\u3092\u8aad\u3080