File:Exponentia spirals.svg
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Summary
[edit]DescriptionExponentia spirals.svg |
English: Exponential spirals. For explanation by Tetyana Butler [1] |
Date | |
Source | Own work |
Author | Adam majewski |
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
Summary
[edit]Here are 3 spirals
x = radius^t*cos(t) y = radius^t*sin(t)
where angle t in radians is changing from tMin to tMax.
Difference between spirals :
- radius r > 1 ( escapes to infinity )
- radius r = 1 ( rotation on unit circle )
- radius r < 1 ( attracts to center z = 0 )
It can be a model[2] of dynamics under complex quadratic polynomial
Maxima CAS source code
[edit]kill(all)$ remvalue(all)$ /* for starting point = e^t use tMin = 1 */ GiveParametric(radius, tMin,tMax) := parametric(radius^t*cos(t),radius^t*sin(t),t,tMin,tMax)$ compile(all); exterior:GiveParametric(1.05, 1, 6*%pi)$ interior:GiveParametric(0.90, 1, 12*%pi)$ boundary:GiveParametric(1.0, 1, 1+2*%pi)$ draw2d(file_name = "expospirals", pic_width=1000, pic_height= 1000, terminal = 'svg, title = "Exponential Spirals", user_preamble = "set grid polar ; set size square; set size square;set key out;set key top right ;set xtics 0.5; set mxtics 0.5 ", nticks = 200, xrange = [-2,2], yrange = [-2,2], color = blue, line_width = 3, key = "radius <1", interior, key = "radius > 1", color = green, exterior, key = "radius = 1", color = red, boundary )$
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:52, 22 October 2012 | 1,000 × 1,000 (25 KB) | Soul windsurfer (talk | contribs) | {{Information |Description ={{en|1=Exponentia spirals}} |Source ={{own}} |Author =Adam majewski |Date =2012-10-12 |Permission = |other_versions = }} |
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Image title | Produced by GNUPLOT 4.4 patchlevel 2 |
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Height | 1000 |