File:Sqrt2.png
Original file (1,072 × 621 pixels, file size: 11 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionSqrt2.png |
English: 3D diagram of square root of real number ( positive and negative)
Polski: Wykres 3D kwadratowego pierwiastka z liczby rzeczywistej ( dodatniej i ujemnej) |
Date | |
Source | Own work |
Author | Adam majewski |
Summary
[edit]This diagram shows function (red 3D curve):
Gray 2D lines are projections of 3D red curve on 2D planes.
One can see that red curve consist of 2 parabolas rotated with respect to themselves ( 90 degrees)
Software needed
[edit]The image was made using
- Maxima CAS program
- draw package archive copy at the Wayback Machine by Mario Rodriguez Riotorto ( interface to Gnuplot)
- Gnuplot
Tested on versions:
- wxMaxima 0.7.6
- Maxima 5.16.3
- Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
- Gnuplot Version 4.2 patchlevel 3
After running below batch file image was created on the screen. It was manually rotated, copied to clipboard, pasted to Paint program. Some interrupted gray lines were added.
Discusion
[edit]Is it a explanation of period doubling ?
"It is an explanation of the shape of the curves in period doubling, but there is more behind period doubling. E.g., when the multiplier of an n-periodic point z is -1, then the equation for period 2*n has a multiple solution. " Wolf Jung
Maxima source code
[edit]/* functions for computing */ give_beta(_c):= sqrt(_c) $ give_alfa(_c):= -sqrt(_c) $ /* c */ xMax:1; xMin:-1; /* re(s) */ yMin:-2; yMax:2; /* im(s) */ zMin:-3; zMax:3; iXmax:1000; dx:(xMax-xMin)/iXmax; p1_alfa:[]; p1_beta:[]; re_c:[]; im_c:[]; re_im:[]; for c:xMin step dx thru xMax do ( alfa:give_alfa(c), p1_alfa:cons([c,realpart(alfa),imagpart(alfa)],p1_alfa), re_c:cons([c,realpart(alfa),zMin],re_c), im_c:cons([c,-2,imagpart(alfa)],im_c), re_im:cons([-1,realpart(alfa),imagpart(alfa)],re_im), beta:give_beta(c), p1_beta:cons([c,realpart(beta),imagpart(beta)],p1_beta), re_c:cons([c,realpart(beta),zMin],re_c), im_c:cons([c,-2,imagpart(beta)],im_c), re_im:cons([-1,realpart(beta),imagpart(beta)],re_im) ); load(draw); draw3d( user_preamble="set ticslevel 0;", terminal = screen, pic_height= iXmax, title = "square roots s= sqrt(c) of real number c ", ylabel = "Re(sqrt(c))", zlabel ="Im(sqrt(c))", xlabel = "c", yrange = [yMin,yMax], zrange = [zMin,zMax], point_type = filled_circle, /* */ points_joined = false, color=gray, point_size = 0.1, points(re_c), points(im_c), points(re_im), /* */ point_size = 0.2, points_joined = true, color = red, points(p1_beta), points(p1_alfa), /* grid and tics */ xtics = {-2,-1,0,1,2}, xtics_rotate = true, ytics = {-2,-1,0,1,2}, ztics ={-2,-1,0,1,2}, grid = true /* draw grid*/ )$
Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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 |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:05, 11 July 2009 | 1,072 × 621 (11 KB) | Soul windsurfer (talk | contribs) | {{Information |Description={{en|1=3D diagram of square root of real number ( positive and negative)}} {{pl|1=Wykres 3D kwadratowego pierwiastka z liczby rzeczywistej ( dodatniej i ujemnej)}} |Source=Own work by uploader |Author=[[User:Adam majewski|Adam m |
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