How can I simulate a beating heart?

Try this pulse animation:

CABasicAnimation *theAnimation;
theAnimation=[CABasicAnimation animationWithKeyPath:@"transform.scale"];
theAnimation.duration=0.7;
theAnimation.repeatCount=HUGE_VALF;
theAnimation.autoreverses=YES;
theAnimation.fromValue=[NSNumber numberWithFloat:1.0];
theAnimation.toValue=[NSNumber numberWithFloat:0.7];
theAnimation.timingFunction=[CAMediaTimingFunction functionWithName:kCAMediaTimingFunctionEaseIn];
[self.heart.layer addAnimation:theAnimation forKey:@"animateOpacity"];

/**
 Heart beating animation
 */
func addHeartBeatAnimation () {
    let beatLong: CABasicAnimation = CABasicAnimation(keyPath: "transform.scale")
    beatLong.fromValue = NSValue(CGSize: CGSizeMake(1, 1))
    beatLong.toValue = NSValue(CGSize: CGSizeMake(0.7, 0.7))
    beatLong.autoreverses = true
    beatLong.duration = 0.5
    beatLong.beginTime = 0.0

    let beatShort: CABasicAnimation = CABasicAnimation(keyPath: "transform.scale")
    beatShort.fromValue = NSValue(CGSize: CGSizeMake(1, 1))
    beatShort.toValue = NSValue(CGSize: CGSizeMake(0.5, 0.5))
    beatShort.autoreverses = true
    beatShort.duration = 0.7
    beatShort.beginTime = beatLong.duration
    beatLong.timingFunction = CAMediaTimingFunction(name: kCAMediaTimingFunctionEaseIn )

    let heartBeatAnim: CAAnimationGroup = CAAnimationGroup()
    heartBeatAnim.animations = [beatLong, beatShort]
    heartBeatAnim.duration = beatShort.beginTime + beatShort.duration
    heartBeatAnim.fillMode = kCAFillModeForwards
    heartBeatAnim.removedOnCompletion = false
    heartBeatAnim.repeatCount = FLT_MAX
    self.layer.addAnimation(heartBeatAnim, forKey: nil)
}

Based on BCBlanka's answer, little more realistic animation

So far I have it so the heart changes size every second, but I want it to be more realistic.

The obvious suggestion is to use a sequence of images, to give you a "smooth" animation.