1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
|
/*
* The MIT License (MIT)
*
* Copyright (c) 2015 Camil Staps <info@camilstaps.nl>
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package com.camilstaps.mandelbrot;
import java.util.HashMap;
import java.util.Map;
/**
* Class for calculating Mandelbrot numbers
* By remembering seen numbers, we can significantly decrease calculation time
*
* @author Camil Staps
*/
public class MandelbrotFractal {
/**
* Storage for previously calculated numbers
*/
private static final Map<Point,Result> mandelNumbers = new HashMap<>();
/**
* Calculate the Mandelbrot number for a specific point up to some maximum
* @param x the x coordinate of the point
* @param y the y coordinate of the point
* @param repetitions the maximum
* @return the mandelbrot number
*/
public synchronized static int mandelNumber(double x, double y, int repetitions) {
Point p = new Point(x, y);
return mandelNumber(p, repetitions);
}
/**
* Calculate the Mandelbrot number for a specific point up to some maximum
* @param p the point
* @param repetitions the maximum
* @return the mandelbrot number
*/
public synchronized static int mandelNumber(Point p, int repetitions) {
if (mandelNumbers.containsKey(p)) {
Result result = mandelNumbers.get(p);
if (repetitions < result.repetitions ||
result.mandelNumber < result.repetitions) {
return result.mandelNumber;
} else {
calculateMandelNumber(p, repetitions, result);
return result.mandelNumber;
}
} else {
Result result = calculateMandelNumber(p, repetitions);
mandelNumbers.put(p, result);
return result.mandelNumber;
}
}
/**
* Calculate the Mandelbrot number for a specifc point up to some maximum
* @param p the point
* @param repetitions the maximum
* @return the result
*/
protected synchronized static Result calculateMandelNumber(Point p, int repetitions) {
Result start = new Result();
start.x = p.x;
start.y = p.y;
calculateMandelNumber(p, repetitions, start);
return start;
}
/**
* Calculate the Mandelbrot number for a specific point up to some maximum,
* starting from an earlier result
* @param p the point
* @param repetitions the maximum
* @param start the earlier result; will be updated with the new result
*/
protected synchronized static void calculateMandelNumber(Point p, int repetitions, Result start) {
int n = start.repetitions;
while (start.x * start.x + start.y * start.y <= 4 && n < repetitions) {
double new_x = start.x * start.x - start.y * start.y + p.x;
start.y = 2 * start.x * start.y + p.y;
start.x = new_x;
n++;
}
start.mandelNumber = n;
}
/**
* A point on a coordinate system
*/
public static class Point {
double x, y;
public Point(double x, double y) {
this.x = x;
this.y = y;
}
@Override
public boolean equals(Object another) {
if (another == null || another.getClass() != Point.class) {
return false;
}
Point that = (Point) another;
return that.x == x && that.y == y;
}
@Override
public int hashCode() {
int hash = 7;
hash = 97 * hash + (int) (Double.doubleToLongBits(this.x) ^ (Double.doubleToLongBits(this.x) >>> 32));
hash = 97 * hash + (int) (Double.doubleToLongBits(this.y) ^ (Double.doubleToLongBits(this.y) >>> 32));
return hash;
}
@Override
public String toString() {
return String.format("(%f,%f)", x, y);
}
}
/**
* A Mandelbrot result consists of a point, the mandelbrot number and the
* maximum with which we calculated that result.
*/
protected static class Result {
int mandelNumber = -1, repetitions = 0;
double x, y;
}
}
|
