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File:Henon bifurcation map b=0.3.png

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Original file(3,150 × 2,200 pixels, file size: 915 KB, MIME type: image/png)

Summary

Description
Henon bifurcation diagram with b = 0.3. The image was created using Mathematica by determining the value of a for each pixel (i.e., the width in a space for each pixel). This width was subdivided into 7 parts where each of the seven parts corresponded to the same pixel column but had slightly different values for a. For x the starting value depended on which of the 7 values for a was used in that pixel column. The x range (-1.5 to 1.5) was divided into 7 equidistant values, For each value of x, 7 distinct values for y were selected to obtain a broad range of starting values. The process of subdividing each pixel column into 7 parts was repeated for each pixel column in the map (2400 times). After throwing away the first 2000 iterations, the next 1,000,000 were used to create the plot. Each time a value fell into an [x,a] pixel, that pixel was incremented by 1. The max value allowed for each pixel was 350,000. After each pixel column was calculated, the column was divided by the maximum value in that column (could be less than 350,000) to get a scale from 0 to 1. Axis were then added to the final map. Altogether 112,000,000,000 iterations were used to generate this map. Calculation time was approximately 2.5 hours.
Date
Source Own work Created with Mathematica
Author Jordan Pierce

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I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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9 September 2011

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Date/TimeThumbnailDimensionsUserComment
current12:58, 10 September 2011Thumbnail for version as of 12:58, 10 September 20113,150 × 2,200 (915 KB)EfecretionCorrected ''a'' scale.
12:45, 10 September 2011Thumbnail for version as of 12:45, 10 September 20113,150 × 2,200 (911 KB)EfecretionMore detail added (better starting positions)
22:21, 9 September 2011Thumbnail for version as of 22:21, 9 September 20113,150 × 2,200 (881 KB)Efecretion{{Information |Description ={{en|1=Henon bifurcation diagram with <i>b</i> = 0.3. The image was created using Mathematica by determining the value of <i>a</i> for each pixel (i.e., the width in <i>a</i> space for each pixel). This width was subdivide
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