File:Parabolic critical orbit of rational function ( Blaschke fraction).png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Parabolic_critical_orbit_of_rational_function_(_Blaschke_fraction).png (600 × 600 pixels, file size: 19 KB, MIME type: image/png)
File information
Structured data
Captions
Summary
[edit]DescriptionParabolic critical orbit of rational function ( Blaschke fraction).png |
English: Parabolic critical orbit of rational function ( Blaschke fraction) f(z) = rho * z^2 * (z-3)/(1-3*z) where rho = -0.6170144002709304 +0.7869518599370003*%i ( cusp ) |
Date | |
Source | Own work |
Author | Adam majewski |
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
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]/* [0.7121885831301268*%i-0.7019881922504848, 0.6038629905954274*%i+0.7970881310050664, (-0.8738242051822692*%i)-0.4862419751909308, 0.7121885831301268*%i-0.701988192250485] */ kill(all); display2d:false; ratprint : false; /* remove "rat :replaced " */ /* 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:[z], for i:1 thru OrbitLength step 1 do ( z:expand(f(z)), if cabs(z) > 2 then ( print(z0), print("orbit of is escaping"), return(Orbit)), Orbit:endcons(z ,Orbit) ), print(z0), print("orbit is not escaping"), return(Orbit) )$ /* f(z) is used as a global function I do not know how to put it as a argument */ GiveOneArmOrbit(z0,OrbitLength):= block( [z,Orbit], z:z0, Orbit:[z], for i:1 thru OrbitLength step 1 do ( z:expand(f(z)), if cabs(z) > 2 then ( print(z0), print("orbit of is escaping"), return(Orbit)), Orbit:endcons(z ,Orbit) ), print(z0), print("orbit is not escaping"), return(Orbit) )$ /* converts angle in radians in range -Pi to Pi to turns */ GiveTurn(a):= ( if a<0 then a:a+2*%pi, /* from range (-Pi,Pi) to range (0,2Pi) */ float(a/(2*%pi)) /* from radians to turns */ )$ /* give turn of complex number z */ cturn(z):=GiveTurn(carg(z))$ /* give Draw List from one point*/ /* converts complex number z = x*y*%i to the list in a draw format: [x,y] */ d(z):=[float(realpart(z)), float(imagpart(z))]$ ToPoint(z):= points([d(z)])$ /* give Draw List from one point*/ ToPoints(myList):= points(map(d,myList))$ compile(all); radius : 1.0; t:1/3; rho : -0.6170144002709304 +0.7869518599370003*%i; f(z):= float(rectform((rho * z^2 * (z-3)/(1-3*z))))$ dz: diff(f(z),z,1); iLength:10000; Orbit: GiveOneArmOrbit(1.0,iLength)$ /* period 3 points */ e: f(f(f(z))) = z$ load (to_poly_solve); s: to_poly_solve (e,z); s: args(s); /* https://stackoverflow.com/questions/12834709/create-a-union-into-a-list-in-maxima */ s:flatten(s); s:map(rhs,s); r:[]; for z in s do if (abs(abs(z) -1) < 0.1) then r:cons(z,r); cycle1:[]; z:r[1]; cycle1: cons(z, cycle1); for i:1 thru 3 step 1 do ( z:float(rectform(f(z))), cycle1:cons(z, cycle1) ); turns:map(cturn,cycle1); Orbit : ToPoints(Orbit)$ r:ToPoints(r)$ z32: ToPoint(cycle1[2]); z31: ToPoint(cycle1[1]); z33: ToPoint(cycle1[3]); zcr: ToPoint(1); cycle1: ToPoints(cycle1)$ load(draw); /* ( interface to gnuplot ) by Mario Rodriguez Riotorto http://www.telefonica.net/web2/biomates */ draw2d( title = "Parabolic period 3 orbit for f(z)= rho * z^2 * (z-3)/(1-3*z))", terminal = png, user_preamble = "set size square; set key left top;", /* 360/26=13.85 ; 360/(2*26)=6,923 */ file_name = concat("~/Dokumenty/julia_blaszke/period3/maxima/cycle_check/1over3/", concat("cycles_j_",string(iLength))), dimensions = [600, 600], /* Since Maxima 5.23, pic_width and pic_height are deprecated. */ yrange = [-1.2,1.2], xrange = [-1.2, 1.2], xlabel = "z.re ", ylabel = "z.im", line_width = 1, nticks = 50, color = gray, transparent = true, ellipse(0,0,1,1,0,360), /* unit circle */ point_type = filled_circle, points_joined = true, point_size = 1.2, key="periodic points", color = red , cycle1, points_joined = false, point_size = 1.2, key="critical point", color = blue , zcr, point_size = 0.8, points_joined = false, key="critical orbit ", color = black , Orbit );
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:24, 20 June 2022 | 600 × 600 (19 KB) | Soul windsurfer (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikibooks.org
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 |