Zig Zag Indicator UPD: Cycle DualityNVIDIA CorporationBATS:NVDAfractIn some earlier works I've mentioned how Markets follow Brownian Motion that explains its probabilistic memory and denies geometric one. And with the recent update of Zig Zag that monitors both directive and temporal aspect of the swings, I'd like to return to review that subject again. Recap of Known Contradicting Theories Brownian motion is a random walk, often used as a model for stock price movements. In its simplest form, it assumes that price changes are independent and identically distributed with a normal distribution. However, financial markets exhibit trends, cycles, and volatility clustering, which are not captured by simple Brownian motion. Benoit Mandelbrot studied the fractal nature of financial markets. He proposed that markets are better modeled using fractal geometry and that price movements exhibit: Fat tails: Extreme events occur more frequently than predicted by the normal distribution. Long-term dependence: Price changes are not independent; there is persistence in volatility and sometimes in returns. Self-similarity: Market patterns repeat at different time scales. Why measuring both H2H and L2L cycles matters: (Please do not confuse with directional swing HH LH LL HL, as they are of trend's price motion and not temporal!) Basic Thoughts The traditional way to measure cycles is through a systematic 𖼆 movements, so that the time distance between Lows counts as cycle length. The best way to fool myself would be to just stick with one method of tracking market rhythms. So, having second perspective of what cycle is, through inverse time count 𖼓 (H ➔ H), would technically back the original one or even challenge at times, which by definition increases awareness of the price fluctuation. We figured that markets move in alternating phases of accumulation and distribution, that's why only measuring one gives half the story. Cycle Confirmation: When H2H and L2L cycles align in duration, it suggests stable, rhythmic market behavior. Divergences signal potential trend changes. Phase Relationships: The timing between highs and lows reveals market temperament: Short 𖼆 + Long 𖼓 = Strong uptrend Short 𖼓 + Long 𖼆 = Strong downtrend Similar durations = Consolidation/balanced market Brownian Motion Contrast By default assumes H2H ≈ L2L (durations symmetry) Random phase relationships No persistent asymmetries The indicator's value comes from measuring exactly what Brownian motion cannot explain. I'm essentially interested in building a temporal map of market psychology rather than just a price map. The dual aspects of timing would letting you see the complete waveform rather than just half of it. The next update would probably be after carefully linking normalized Averaged(True Range/close*100) to the directional wave, in order to reveal how price swings are naturally scaled. It might give some constants which could be used for modeling.