File:Critical orbit f(z) = z*z+ 0.28+0.0113*i.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
![File:Critical orbit f(z) = z*z+ 0.28+0.0113*i.png](https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Critical_orbit_f%28z%29_%3D_z%2Az%2B_0.28%2B0.0113%2Ai.png/600px-Critical_orbit_f%28z%29_%3D_z%2Az%2B_0.28%2B0.0113%2Ai.png?20210807122011)
Size of this preview: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 1,000 × 1,000 pixels.
Original file (1,000 × 1,000 pixels, file size: 84 KB, MIME type: image/png)
File information
Structured data
Captions
Captions
Critical orbit f(z) = z*z+ 0.28+0.0113*i
Summary
[edit]DescriptionCritical orbit f(z) = z*z+ 0.28+0.0113*i.png |
English: Critical orbit f(z) = z*z+ 0.28+0.0113*i. Location by Njarlatotep at Russian Wikipedia. internal radius(c)= 0.9999653149513355, internal angle(c)= 0.05730221983248095 |
Date | |
Source | Own work |
Author | Adam majewski |
Other versions |
|
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- 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.
Maxima CAS src code
[edit]kill(all); remvalue(all); /*------------- functions definitions ---------*/ /* function */ f(z):=z^2 + c; define (df(z), diff(f(z), z, 1))$ /* f(z) is used as a global function I do not know how to put it as a argument */ GiveOrbit(z0,OrbitLength):= block( [z,Orbit], z:z0, Orbit:[z0], for i:1 thru OrbitLength step 1 do ( z:expand(f(z)), Orbit:endcons(z,Orbit)), return(Orbit) )$ /* converts complex number z = x*y*%i to the list in a draw format: [x,y] */ d(z):=[float(realpart(z)), float(imagpart(z))]$ ToPoints(myList):= points(map('d,myList))$ /* give Draw List from one point*/ ToPoint(z):=points([d(z)])$ cturn(z):=block( [t], t : carg(z), t : t/(2*%pi), if (t<0.0) then t:t+1.0, return(float(t)) )$ compile(all); /* -----const values ------- */ c: 0.28+0.0113*%i$ zcr:0.0$ iLength:100000; /* ------------- main = computations -----------------*/ /* compute fixed points */ Beta:float(rectform((1+sqrt(1-4*c))/2))$ /* compute repelling fixed point beta */ alfa:float(rectform((1-sqrt(1-4*c))/2))$ /* other fixed point */ m: df(alfa); print("multiplicator(alfa)=", float(rectform(m)))$ print("stability(alfa)=", cabs(m))$ print("internal angle(alfa)=", cturn(alfa))$ Orbit:GiveOrbit(zcr,iLength)$ Orbit:ToPoints(Orbit)$ zcr:ToPoint(zcr)$ alfa:ToPoint(alfa)$ /*-----------------------------------------------------------------------*/ path:"~/Dokumenty/cr/"$ /* if empty then file is in a home dir */ load(draw); /* ( interface to gnuplot ) by Mario Rodriguez Riotorto http://www.telefonica.net/web2/biomates */ draw2d( title = concat("Critical orbit for f(z)=z^2 +", string(c)), terminal = png, user_preamble = "set size square", /* */ file_name = concat(path ,string(iLength),"_joined"), dimensions = [1000,1000], /* Since Maxima 5.23, pic_width and pic_height are deprecated. */ /* xrange = [-0.8,0.0], yrange = [-0.4,0.4], */ xlabel = "z.re ", ylabel = "z.im", point_type = 7, points_joined = true, point_size = 0.8, key=" critical orbit ", color =red, Orbit, point_size = 1.2, key= "critical point", color = blue, zcr, key= "fixed point", color = black, alfa );
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:20, 7 August 2021 | ![]() | 1,000 × 1,000 (84 KB) | Soul windsurfer (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following 3 pages use this file:
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Horizontal resolution | 37.8 dpc |
---|---|
Vertical resolution | 37.8 dpc |