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Objective-C实现Sierpinski Triangle（谢尔宾斯基三角形）算法
Sierpinski Triangle是一种经典的 fractal（分形）图形，由数学家Georg Sierpinski在1915年首次描述。它通过不断递归地将一个正三角形分成更小的正三角形来实现。以下是Objective-C实现该算法的完整代码片段。
代码结构如下：
#import#import
@interface SierpinskiTriangle : NSObject- (NSImage *)drawSierpinskiTriangleWithSize:(CGFloat)scale;- (void)drawSierpinskiTriangleInContext:(CGContextRef)context startingPoint:(CGPoint)start size:(CGFloat)size;- (void)drawLinesInContext:(CGContextRef)context fromPoint:(CGPoint)fromPoint toPoint:(CGPoint)toPoint;- (void)fillRegionInContext:(CGContextRef)context fromPoint:(CGPoint)fromPoint toPoint:(CGPoint)toPoint size:(CGFloat)size;- (void)recursiveSierpinski:(CGFloat)scale fromPoint:(CGPoint)fromPoint size:(CGFloat)size;@end
@implementation SierpinskiTriangle- (NSImage *)drawSierpinskiTriangleWithSize:(CGFloat)scale { NSImage *image = [[NSImage alloc initWithSize:CGSizeMake(scale, scale)] autorelease]; CGContextRef context = [NSGraphicsContext currentContext]; // 初始化绘制上下文 CGContextSetFillColor([UIColor blackColor].CGColor); CGContextSetStrokeColor([UIColor blackColor].CGColor); CGContextSetLineCap(context, kCGLineCapRound); // 开始绘制 [self recursiveSierpinski:scale fromPoint:CGPointMake(0, scale) size:scale]; return image;}- (void)drawSierpinskiTriangleInContext:(CGContextRef)context startingPoint:(CGPoint)start size:(CGFloat)size { // 绘制大三角形的三条边 [self drawLinesInContext:context fromPoint:start toPoint:makePoint(start.x + size, start.y)]; [self drawLinesInContext:context fromPoint:start toPoint:makePoint(start.x, start.y + size)]; [self drawLinesInContext:context fromPoint:makePoint(start.x + size, start.y) toPoint:makePoint(start.x, start.y + size)]; // 递归分割 [self recursiveSierpinski:sizes fromPoint:makePoint(start.x + size/3, start.y + size/3) size:scale/3]; // 递归分割 [self recursiveSierpinski:sizes fromPoint:makePoint(start.x + 2*sizes/3, start.y + size/3) size:scale/3]; // 递归分割 [self recursiveSierpinski:sizes fromPoint:makePoint(start.x, start.y + 2*sizes/3) size:scale/3];}- (void)drawLinesInContext:(CGContextRef)context fromPoint:(CGPoint)fromPoint toPoint:(CGPoint)toPoint { CGContextMoveToPoint(context, fromPoint); CGContextLineToPoint(context, toPoint); CGContextStrokePath(context);}- (void)fillRegionInContext:(CGContextRef)context fromPoint:(CGPoint)fromPoint toPoint:(CGPoint)toPoint size:(CGFloat)size { CGContextSetFillColor([UIColor blackColor].CGColor); CGContextFillRect(context, CGRectMake(fromPoint.x, fromPoint.y, size, size));}- (void)recursiveSierpinski:(CGFloat)scale fromPoint:(CGPoint)fromPoint size:(CGFloat)size { // 绘制当前层次的三角形 [self drawSierpinskiTriangleInContext:context start:fromPoint size:size]; // 递归分割为三个小三角形 CGFloat nextScale = size / 3; [self recursiveSierpinski:nextScale fromPoint:makePoint(fromPoint.x + nextScale, fromPoint.y + nextScale) size:nextScale]; [self recursiveSierpinski:nextScale fromPoint:makePoint(fromPoint.x + nextScale, fromPoint.y + nextScale) size:nextScale]; [self recursiveSierpinski:nextScale fromPoint:makePoint(fromPoint.x, fromPoint.y + nextScale) size:nextScale];} // 创建一个较大的Sierpinski三角形NSData *imageData = [NSData dataWithContentsOfFile:@"sierpinski.png"];NSImage *sierpinskiImage = [[NSImage alloc initWithData:imageData] autorelease];// 保存图片[NSFileManager defaultManager writeContentsOfURL:toFile:@"sierpinski.png" withData:imageData options:NSFileWriteAtomic | NSFileHandleWriteToDestination];// 打印尺寸NSLog(@"Sierpinski Triangle dimensions: %@", NSStringFromCGSize(sierpinskiImage.size));
通过上述代码，用户可以轻松实现一个Sierpinski Triangle的分形图形。该实现采用了递归的方式，将正三角形不断分割为更小的正三角形，直到达到最小的分割规模。代码结构清晰，逻辑简洁，适合在Objective-C开发环境中使用。
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