René's URL Explorer Experiment

Title: GitHub - ratwolfzero/hopalong_python: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor

Open Graph Title: GitHub - ratwolfzero/hopalong_python: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor

X Title: GitHub - ratwolfzero/hopalong_python: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor

Description: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor - ratwolfzero/hopalong_python

Open Graph Description: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor - ratwolfzero/hopalong_python

X Description: Generative Density Approximation for Deterministic Point Patterns: The Hopalong Attractor - ratwolfzero/hopalong_python

Mail addresses
ratwolf@duck.com

Opengraph URL: https://github.com/ratwolfzero/hopalong_python

X: @github

direct link

Domain: github.com

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23 Commits	https://github.com/ratwolfzero/hopalong_python/commits/main/
	https://github.com/ratwolfzero/hopalong_python/commits/main/
Alternative_Solutions	https://github.com/ratwolfzero/hopalong_python/tree/main/Alternative_Solutions
Alternative_Solutions	https://github.com/ratwolfzero/hopalong_python/tree/main/Alternative_Solutions
Documentation	https://github.com/ratwolfzero/hopalong_python/tree/main/Documentation
Documentation	https://github.com/ratwolfzero/hopalong_python/tree/main/Documentation
Experimental_Dev	https://github.com/ratwolfzero/hopalong_python/tree/main/Experimental_Dev
Experimental_Dev	https://github.com/ratwolfzero/hopalong_python/tree/main/Experimental_Dev
Output	https://github.com/ratwolfzero/hopalong_python/tree/main/Output
Output	https://github.com/ratwolfzero/hopalong_python/tree/main/Output
Statistics	https://github.com/ratwolfzero/hopalong_python/tree/main/Statistics
Statistics	https://github.com/ratwolfzero/hopalong_python/tree/main/Statistics
.gitignore	https://github.com/ratwolfzero/hopalong_python/blob/main/.gitignore
.gitignore	https://github.com/ratwolfzero/hopalong_python/blob/main/.gitignore
LICENSE	https://github.com/ratwolfzero/hopalong_python/blob/main/LICENSE
LICENSE	https://github.com/ratwolfzero/hopalong_python/blob/main/LICENSE
README.md	https://github.com/ratwolfzero/hopalong_python/blob/main/README.md
README.md	https://github.com/ratwolfzero/hopalong_python/blob/main/README.md
hopalong_basic.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_basic.py
hopalong_basic.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_basic.py
hopalong_basic_2D_3D.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_basic_2D_3D.py
hopalong_basic_2D_3D.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_basic_2D_3D.py
hopalong_extended.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_extended.py
hopalong_extended.py	https://github.com/ratwolfzero/hopalong_python/blob/main/hopalong_extended.py
README	https://github.com/ratwolfzero/hopalong_python
MIT license	https://github.com/ratwolfzero/hopalong_python
	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_0.png
Calculate & Visualize the Hopalong Attractor with Python	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
Abstract	https://github.com/ratwolfzero/hopalong_python#abstract
Historical Context	https://github.com/ratwolfzero/hopalong_python#historical-context
The Hopalong Attractor Functions	https://github.com/ratwolfzero/hopalong_python#the-hopalong-attractor-functions
Computational Approach	https://github.com/ratwolfzero/hopalong_python#computational-approach
Requirements	https://github.com/ratwolfzero/hopalong_python#requirements
Usage	https://github.com/ratwolfzero/hopalong_python#usage
Input	https://github.com/ratwolfzero/hopalong_python#input
Output	https://github.com/ratwolfzero/hopalong_python#output
Features, Functionality, and Special Scenarios	https://github.com/ratwolfzero/hopalong_python#features-functionality-and-special-scenarios
Program Variants	https://github.com/ratwolfzero/hopalong_python#program-variants
Pixel-Based Density Approximation	https://github.com/ratwolfzero/hopalong_python#pixel-based-density-approximation
Comparison of Pixel-Based Density Approximation vs. Histogram-Based Density Estimation	https://github.com/ratwolfzero/hopalong_python#comparison-of-pixel-based-density-approximation-vs-histogram-based-density-estimation
Pixel-Based Approximation	https://github.com/ratwolfzero/hopalong_python#pixel-based-approximation
Histogram-Based Estimation	https://github.com/ratwolfzero/hopalong_python#histogram-based-estimation
Visualization of Aggregated Density Distribution	https://github.com/ratwolfzero/hopalong_python#visualization-of-aggregated-density-distribution
Summary	https://github.com/ratwolfzero/hopalong_python#summary
Conclusions	https://github.com/ratwolfzero/hopalong_python#conclusions
Application of Copysign (Math Module) as a Signum Function	https://github.com/ratwolfzero/hopalong_python#application-of-copysign-math-module-as-a-signum-function
Special Constellations and Edge Cases of the Attractor	https://github.com/ratwolfzero/hopalong_python#special-constellations-and-edge-cases-of-the-attractor
Optional Features	https://github.com/ratwolfzero/hopalong_python#optional-features
Performance Optimization	https://github.com/ratwolfzero/hopalong_python#performance-optimization
Just-In-Time Compilation (JIT)	https://github.com/ratwolfzero/hopalong_python#just-in-time-compilation-jit
Dummy Calls	https://github.com/ratwolfzero/hopalong_python#dummy-calls
Parallelization and Race Conditions	https://github.com/ratwolfzero/hopalong_python#parallelization-and-race-conditions
Two-Pass Approach	https://github.com/ratwolfzero/hopalong_python#two-pass-approach
Two-Pass Code Section	https://github.com/ratwolfzero/hopalong_python#two-pass-code-section
Alternative Solutions	https://github.com/ratwolfzero/hopalong_python#alternative-solutions
One-Pass Approach with Full Trajectory Caching*	https://github.com/ratwolfzero/hopalong_python#one-pass-approach-with-full-trajectory-caching
One-Pass Approach with Limited Memory Usage (Chunked or No Caching)*	https://github.com/ratwolfzero/hopalong_python#one-pass-approach-with-limited-memory-usage-chunked-or-no-caching
Potentially Other, More Sophisticated Solutions	https://github.com/ratwolfzero/hopalong_python#potentially-other-more-sophisticated-solutions
Recap	https://github.com/ratwolfzero/hopalong_python#recap
Recent Code Changes	https://github.com/ratwolfzero/hopalong_python#recent-code-changes
Enjoy the Exploration	https://github.com/ratwolfzero/hopalong_python#enjoy-the-exploration
License	https://github.com/ratwolfzero/hopalong_python#license
References	https://github.com/ratwolfzero/hopalong_python#references
References for Python Libraries and Modules	https://github.com/ratwolfzero/hopalong_python#references-for-python-libraries-and-modules
Mathematical Appendix	https://github.com/ratwolfzero/hopalong_python#mathematical-appendix
Notations for Pixel-Based Density Approximation	https://github.com/ratwolfzero/hopalong_python#notations-for-pixel-based-density-approximation
Continuous to Discrete Mapping	https://github.com/ratwolfzero/hopalong_python#continuous-to-discrete-mapping
Tracking of Density Accumulation	https://github.com/ratwolfzero/hopalong_python#tracking-of-density-accumulation
Total Hit Count	https://github.com/ratwolfzero/hopalong_python#total-hit-count
	https://github.com/ratwolfzero/hopalong_python#abstract
	https://github.com/ratwolfzero/hopalong_python#historical-context
2	https://github.com/ratwolfzero/hopalong_python#references
3	https://github.com/ratwolfzero/hopalong_python#references
	https://github.com/ratwolfzero/hopalong_python#the-hopalong-attractor-functions
2	https://github.com/ratwolfzero/hopalong_python#references
math.copysign()	https://github.com/ratwolfzero/hopalong_python#application-of-copysign-math-module-as-a-signum-function
	https://github.com/ratwolfzero/hopalong_python#computational-approach
Pixel-Based Density Approximation	https://github.com/ratwolfzero/hopalong_python#pixel-based-density-approximation
Two-Pass Approach	https://github.com/ratwolfzero/hopalong_python#two-pass-approach
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#requirements
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#usage
	https://github.com/ratwolfzero/hopalong_python#input
	https://github.com/ratwolfzero/hopalong_python#output
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_1.png
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_2.png
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_3.png
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_4.png
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#features-functionality-and-special-scenarios
	https://github.com/ratwolfzero/hopalong_python#program-variants
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#pixel-based-density-approximation
Mathematical Appendix:	https://github.com/ratwolfzero/hopalong_python#mathematical-appendix
	https://github.com/ratwolfzero/hopalong_python#comparison-of-pixel-based-density-approximation-vs-histogram-based-density-estimation
	https://github.com/ratwolfzero/hopalong_python#pixel-based-approximation
	https://github.com/ratwolfzero/hopalong_python#histogram-based-estimation
	https://github.com/ratwolfzero/hopalong_python#visualization-of-aggregated-density-distribution
	https://github.com/ratwolfzero/hopalong_python#summary
Two-Pass Approach	https://github.com/ratwolfzero/hopalong_python#two-pass-approach
	https://github.com/ratwolfzero/hopalong_python#conclusions
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_5.png
Special Constellations and Edge Cases	https://github.com/ratwolfzero/hopalong_python#special-constellations-and-edge-cases-of-the-attractor
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#application-of-copysign-math-module-as-a-signum-function
	https://github.com/ratwolfzero/hopalong_python#special-constellations-and-edge-cases-of-the-attractor
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_6.png
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_7.png
	https://github.com/ratwolfzero/hopalong_python/blob/main/Documentation/Figure_8.png
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#optional-features
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#performance-optimization
	https://github.com/ratwolfzero/hopalong_python#just-in-time-compilation-jit
	https://github.com/ratwolfzero/hopalong_python#dummy-calls
	https://github.com/ratwolfzero/hopalong_python#parallelization-and-race-conditions
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#two-pass-approach
	https://github.com/ratwolfzero/hopalong_python#two-pass-code-section
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#alternative-solutions
	https://github.com/ratwolfzero/hopalong_python#one-pass-approach-with-full-trajectory-caching
	https://github.com/ratwolfzero/hopalong_python#one-pass-approach-with-limited-memory-usage-chunked-or-no-caching
	https://github.com/ratwolfzero/hopalong_python#potentially-other-more-sophisticated-solutions
	https://github.com/ratwolfzero/hopalong_python#recap
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#recent-code-changes
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#enjoy-the-exploration
Also check out my simpler Rust version	https://github.com/ratwolfzero/hopalong
	https://github.com/ratwolfzero/hopalong_python#license
MIT License	https://github.com/ratwolfzero/hopalong_python/blob/main/LICENSE
	https://github.com/ratwolfzero/hopalong_python#references
Back to Abstract	https://github.com/ratwolfzero/hopalong_python#abstract
	https://github.com/ratwolfzero/hopalong_python#references-for-python-libraries-and-modules
NumPy Documentation	https://numpy.org/doc/stable/
Matplotlib Documentation	https://matplotlib.org/stable/contents.html
Numba Documentation	https://numba.readthedocs.io/
Python Built-in Functions	https://docs.python.org/3/library/functions.html
Python Math Module	https://docs.python.org/3/library/math.html
Python Time Module	https://docs.python.org/3/library/time.html#module-time
Python Resource Module	https://docs.python.org/3/library/resource.html
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
	https://github.com/ratwolfzero/hopalong_python#mathematical-appendix
	https://github.com/ratwolfzero/hopalong_python#notations-for-pixel-based-density-approximation
	https://github.com/ratwolfzero/hopalong_python#continuous-to-discrete-mapping
	https://github.com/ratwolfzero/hopalong_python#tracking-of-density-accumulation
	https://github.com/ratwolfzero/hopalong_python#total-hit-count
Back to Pixel-Based Density Approximation	https://github.com/ratwolfzero/hopalong_python#pixel-based-density-approximation
Back to Table of Contents	https://github.com/ratwolfzero/hopalong_python#calculate--visualize-the-hopalong-attractor-with-python
github.com/ratwolfzero/hopalong_python	https://github.com/ratwolfzero/hopalong_python
python	https://github.com/topics/python
dynamics	https://github.com/topics/dynamics
non-linear	https://github.com/topics/non-linear
quantization	https://github.com/topics/quantization
strange-attractors	https://github.com/topics/strange-attractors
deterministic	https://github.com/topics/deterministic
discretization	https://github.com/topics/discretization
density-estimation	https://github.com/topics/density-estimation
attractors	https://github.com/topics/attractors
orbis	https://github.com/topics/orbis
hopalong	https://github.com/topics/hopalong
pixel-based	https://github.com/topics/pixel-based
probability-density-function	https://github.com/topics/probability-density-function
non-linear-dynamics	https://github.com/topics/non-linear-dynamics
generative-methods	https://github.com/topics/generative-methods
barry-martin	https://github.com/topics/barry-martin
hopalong-attractor	https://github.com/topics/hopalong-attractor
emergent-density	https://github.com/topics/emergent-density
density-approximation	https://github.com/topics/density-approximation
martin-map	https://github.com/topics/martin-map
Readme	https://github.com/ratwolfzero/hopalong_python#readme-ov-file
MIT license	https://github.com/ratwolfzero/hopalong_python#MIT-1-ov-file
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Activity	https://github.com/ratwolfzero/hopalong_python/activity
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Releases	https://github.com/ratwolfzero/hopalong_python/releases
Packages 0	https://github.com/users/ratwolfzero/packages?repo_name=hopalong_python
Python 100.0%	https://github.com/ratwolfzero/hopalong_python/search?l=python
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