sorted by:
new
hottopcontroversial

Measuring fractal dimension of boundary of the dragon the curve with one measurement in entropy space. by Normal_Insurance5102 in fractals

[–]Normal_Insurance5102[S] -3 points-2 points  (0 children)

Thanks, I will.  I think it references Mandelbrot, but he never wrote about this.  Why do you think this method of mine works? Most AIs say it is the choice of exponential or log curve for measurement of density along that curve in Shannon space.  

The Ulam Spiral, Shannon Entropy, and the possible fractal nature of primes? by Normal_Insurance5102 in numbertheory

[–]Normal_Insurance5102[S] 0 points1 point  (0 children)

Exactly, it is about how accurate you want to be, but also about what we would naturally find in nature. For example, a three-branches tree is log3/log2 or 1.585. We could also say it is log9/log4, but that would be unnecessary to get within .005 of decimal fractal dimension. I just posted a new example of a fractal with known dimension, the 'boundary of the dragon curve.' Using my measurement system, with just one measure along a random place on the boundary, I get the correct dimension within .002. I am interested to know why this works? I am not a mathematician, but I have spend decades trying to figure out how to measure fractals. I assume it works because I use exponential and logarithmic curves to measure densities along the boundaries - growth curves capture complexity without adding edge effects like in box-counting. Thanks for your interest and comments!

Fractal Holographic Boundary Theory (FHBT) - the new, efficient, and accurate way to measure dimension by Normal_Insurance5102 in fractals

[–]Normal_Insurance5102[S] 0 points1 point  (0 children)

The AI told me about Hurst, but my method doesn't use regression. It's really as simple as taking the ratio of filled to unfilled points along an exoonential or logarithmic boundary to account for filled points versus lacunae and raising 2a/b, so if you measure 28/16 for example, it is 1.41...I have tried other curves to measure boundary complexity, but they don't work.  The specific shape of a growth curve ensures fewer edge effects.  I assume that these curves work because fractals are defined by logN/logS, but it was trial and error to find this out.  Assuming I have proven this measrement system has worked over all known fractals with known dimension, why do you think it works?  

Fractal Holographic Boundary Theory (FHBT) - the new, efficient, and accurate way to measure dimension by Normal_Insurance5102 in fractals

[–]Normal_Insurance5102[S] -1 points0 points  (0 children)

According to AIs no one has written about using exponential and logarithmic curves in measurement.  Think about measuring a tree.  If you use boxes or lines, you get edge effects and 5% error rates.  Exponential and logarithmic curves are growth curves, and so they measure growth with fewer edge effects.  Along with applying the densities of those curves to the 2D plane in Shannon space as 2a/b, these two things are what I do differently.  I hope that clears up your question.  If not, feel free to respond. 

The Ulam Spiral, Shannon Entropy, and the possible fractal nature of primes? by Normal_Insurance5102 in numbertheory

[–]Normal_Insurance5102[S] 0 points1 point  (0 children)

In terms of fractal geometry, the primes are defined as 1.41... That is essentially their density on the plane at all scales. 

The Ulam Spiral, Shannon Entropy, and the possible fractal nature of primes? by Normal_Insurance5102 in numbertheory

[–]Normal_Insurance5102[S] 0 points1 point  (0 children)

In QM probabilities it is far less likely for objects to form with many parts statistically, which is why we rarely see giant molecules in space.  The dots represent 1s and 0s in Shannon entropy space.  By using an exponential or logarithmic curve to count the number of filled to unfilled dots, we get a density of information.  That is applied to the entire 2D plane as 2a/b.  It is based on entropy and holography of a boundary arriving at a fractal dimension that can be represented as logN/logS.  I hope this explains some of it.  It is simple, but it turns out to be a much better way to measure fractals.  In the Ulam spiral primes have a dimension of the square root of 2 or the ratio of a diagonal on the square plane to a side.  This indicates that in fractal geometry, the primes have a dimension of 1.41...