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# www.BillHowell.ca 21Nov2021 initial
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"$d_web"'CompLangs/Fractals/0_Fractal notes.txt'
21Nov2021 Lindenmayer Systems (L-Systems)
21Nov2021 search "fractal models of neurons"
12Nov2021 Fractal computing languages
16Nov2021 http://fractalarts.com/ASF/Fractal_Software_Programs.html
21Nov2021 Mandelbulber - 3D fractals
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#] 21Nov2021 Lindenmayer Systems (L-Systems)
https://fractalfoundation.org/OFC/OFC-2-4.html
https://fractalfoundation.org/OFC/OFC-2-5.html
In this lesson, we will use a java applet, called "Fractal Grower" in a separate window to explore the language of L-Systems. This simple but powerful language allows us to harness the power of iteration to create realistic looking plant-like structures, as well as many other interesting fractals.
Before we launch the Fractal Grower program, we'll look at the basic grammar of the L-System language.
Let's examine the growth of an extremely simplified tree.
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#] 21Nov2021 search "fractal models of neurons"
>> TONS of stuff!!
https://fractalfoundation.org/OFC/OFC-1-6.html
Fractal Neurons
[Search domain fractalfoundation.org] https://fractalfoundation.org › OFC › OFC-1-6.html
It is the fractal branching pattern of the neuron's axons and dendrites that allows them to communicate with so many other cells. If neurons were shaped like cubes and neatly packed into the brain, one neuron could only connect with at most 6 other cells. Hippocampal neurons. Scale approximately 700 microns. Image courtesy of Paul de Koninck ...
http://www.fractogene.com/89_fractal/89_fractal.html
Neural Geometry: Towards a Fractal Model of Neurons
[Search domain fractogene.com] www.fractogene.com › 89_fractal › 89_fractal.html
It is argued that the bifurcation-rule of branching expresses a fractal dimension, and the model reveals some simple codes responsible for generating dendritic arbors. The road towards developing a full structuro-functional fractal model of neurons is certainly long and-as most geometrizations in natural sciences-probably uphill.
https://pubmed.ncbi.nlm.nih.gov/11465996/
Use of fractal theory in neuroscience: methods, advantages ...
[Search domain pubmed.ncbi.nlm.nih.gov] https://pubmed.ncbi.nlm.nih.gov › 11465996
Fractal analysis has already found widespread application in the field of neuroscience and is being used in many other areas. Applications are many and include ion channel kinetics of biological membranes and classification of neurons according to their branching characteristics. In this article we review some practical methods that are now ...
https://www.nature.com/articles/s41598-021-81421-2
How neurons exploit fractal geometry to optimize their ...
[Search domain nature.com] https://www.nature.com › articles › s41598-021-81421-2
Fractal analyses of a wide variety of neurons indicate that their D values don't generally exceed D = 2 17, 23, presumably because of the excessive costs of higher D fractals. For comparison, we ...
(PDF) Neural Geometry: Towards a Fractal Model of Neurons ...
[Search domain researchgate.net] https://www.researchgate.net › publication › 261403245_Neural_Geometry_Towards_a_Fractal_Model_of_Neurons_Chapter_in_Models_of_Brain_Function
Neural Geometry: Towards a Fractal Model of Neurons Chapter in: Models of Brain Function. January 1989. In book: Models in Brain Function (pp.453-464) Publisher: Cambridge University Press ...
Morphology and Fractal-Based Classifications of Neurons ...
[Search domain link.springer.com] https://link.springer.com › chapter › 10.1007 › 978-1-4939-3995-4_6
For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has contributed substantially to classifying functional categories, where in general, the more pathological the biological status, the lower the fractal ...
Fractal analysis reveals subclasses of neurons and ...
[Search domain webcentral.uc.edu] webcentral.uc.edu › eprof › media › attachment › eprofmediafile_3681.pdf
of single neurons in an anesthetized animal model were analyzed via fractal methods. Detrended ﬂuctuation analysis (DFA), a kind of fractal analysis, was utilized to bolster the case for two subclasses of mitral cells.
Fractal Neural Networks
[Search domain fractal.org] www.fractal.org › Life-Science-Technology › Publications › Fractal-Neural-Networks.htm
In principle all trajectories can be interpreted as symbolic representations of neurons . An iteration of a fractal algorithm will move us from z n to z (n+1). As well , a neuron at any point z n in a network could send its activity along its axon ( following the respective trajectory ) to the point z (n+1) of the neural network .
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#] 12Nov2021 Fractal computing languages
http://alvyray.com/Papers/CG/PlantsFractalsandFormalLanguages.pdf
Plants, Fractals, and Formal Languages - Alvy Ray Smith
[Search domain alvyray.com] alvyray.com › Papers › CG › PlantsFractalsandFormalLanguages.pdf
It is based on an extension Of the well-known formal languages Of symbol strings to the lesser-known formal languages of labeled graphs. It is so tempting to describe these plant models as "fractal" that the similarities of this class of models with fractal models are explored in an attempt at rapprochement.
>> saved to "$d_webwe"'Software programming & code/Fractal comptr languages/Smith, Alvy Jul1984 Plants, Fractals, and Formal Languages.pdf
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#] 16Nov2021 http://fractalarts.com/ASF/Fractal_Software_Programs.html
>> great list of programs
LMDE Software manager lists 5-10 fractal software
IJCNN2021 Chinese video about similar to "on-center-off-surround" nice results (best paper?)
>> could really help with bringing functional morphisms to MCode fractal neuron assemblies
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#] 21Nov2021 Mandelbulber - 3D fractals
FracPlanet timday@timday.com, https://fracplanet.sourceforge.net
>> would have to search through source code
>> None are for trees, although I saw links for Mac & PC tree fractals
search "fractal models of neurons"
# enddoc