User:Adam majewski

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Wikipedia-logo.pngWikipedia - my page in wiki

home page. - dead but web archive can help

gitlab

https://tools.wmflabs.org/glamtools/glamorous.php

Wikibooks -en - Adam majewski

My Dropbox public folders

Mathematics Stack Exchange MathOverflow Wikibooks -pl - Adam majewski

My uploads

Photographer Barnstar.png The Photographer's Barnstar
foto

smoke[edit]

relief[edit]

Cartographic

Shaded

Hachures, are a form of shading using lines

Sketchy

with lines

define the colors used for different terrain heights:

map projections[edit]


Digital Image Processing[edit]

  • data analysis
  • image processing
    • image enhacement = process an image so that result is more suitable than original image for specific application
      • Histogram equalization

computer graphic[edit]

www.pling.org.uk/cs/cgv.html
www.tutorialspoint.com/computer_graphics/computer_graphics_curves.htm
github.com/jagregory/abrash-black-book
  pages.mtu.edu/~shene/COURSES/cs3621/NOTES/model/b-rep.html
  pages.mtu.edu/~shene/COURSES/cs3621/NOTES/notes.html

libraries[edit]

graphics pipeline[edit]



2D graphics pipeline[edit]

Steps[1]

  • clipping : covert object in world coordinate to object subset = = applaying world window to object
  • window to vieport mapping
  • rasterisation = (scan conversion) – Convert high level object descriptions to pixel colors in the frame buffer
  • display/ save


realistic 2D static images[edit]

realistic 2D static images [2]

  • Higher pixel resolution ("4k" and "8k").
  • Wider color gamut (WCG) : express a wider range of colors than today ( BT.2020 color gamut )
  • High Dynamic Range (HDR): express a wider range of luminance than today.


Check if you are ready:


icc[edit]

  convert image_rgb.tiff -profile "RGB.icc" -profile "CMYK.icc" image_cmyk.tiff

algorithm[edit]

perceptually accurate rendering algorithm:

  • Render your image using correct radiometric calculations. You trace individual wavelengths of light or buckets of wavelengths. Whatever. In the end, you have an image that has a representation of the spectrum received at every point.
  • At each pixel, you take the spectrum you rendered, and convert it to the CIE XYZ color space. This works out to be integrating the product of the spectrum with the standard observer functions (see CIE XYZ definition).
  • This produces three scalar values, which are the CIE XYZ colors.
  • Use a matrix transform to convert this to linear RGB, and then from there use a linear/power transform to convert linear RGB to sRGB.
  • Convert from floating point to uint8 and save, clamping values out of range (your monitor can't represent them).
  • Send the uint8 pixels to the framebuffer.
  • The display takes the sRGB colors, does the inverse transform to produce three primaries of particular intensities. Each scales the output of whatever picture element it is responsible for. The picture elements light up, producing a spectrum. This spectrum will be (hopefully) a metamer for the original spectrum you rendered.
  • You perceive the spectrum as you would have perceived the rendered spectrum.

hdr[edit]

Steps by Anna Altez

  • Set your ISO to 200, set your camera to Aperture Priority
  • take three photos with exposure settings as EV 0, EV-2, and EV+2. The more differently exposed photos you have, the better.
  • Merge to HDR
  • Select 32-bit/channel and tick Remove Ghosts
  • . Click Image > Mode > 16-bit/channel
  • tone mapping. Adjust the settings depending on how you want your HDR photo to look.

image enhancement techniques[edit]

  • gray-level transformation functions
    • linear (negative and identity transformations)
    • logarithmic (log and inverse-log transformations)
    • power-law (nth power and nth root transformations).T

color[edit]

Color depth[edit]

first floating point number format


Color_depth

  • 1-bit color = binary image
  • 8-bit color = 256 colors, usually from a fully-programmable palette ( VGA)
  • 24-bit = True color

Dynamic range[edit]

Dynamic rang types:

Dynamic range of

  • image
  • display
  • print


HDR and:

color effects[edit]

Shades[edit]

Shades of Color Notice that since (0,0,0) is black and (1,1,1) is white, shades of any particular color are created by moving closer to black or to white. You can use the parametric equation for a linear relationship between two values to make shades of a color darker or lighter.

A parametric equation to calculate a linear change between values A and B:

  C = A + (B-A)*t;  // where t varies between 0 and 1

To change a color (r,g,b) to make it lighter, move it closer to (1,1,1).

  newR = r + (1-r)*t;  // where t varies between 0 and 1
  newG = g + (1-g)*t;  // where t varies between 0 and 1
  newB = b + (1-b)*t;  // where t varies between 0 and 1

To change a color (r,g,b) to make it darker, move it closer to (0,0,0).

  newR = r + (0-r)*t;  // where t varies between 0 and 1
  newG = g + (0-g)*t;  // where t varies between 0 and 1
  newB = b + (0-b)*t;  // where t varies between 0 and 1
  // or
  newR = r*t;  // where t varies between 1 and 0
  newG = g*t;  // where t varies between 1 and 0
  newB = b*t;  // where t varies between 1 and 0

color wheel[edit]

Intermediate Colour Values[edit]

Smooth colouring requires the ability to obtain a colour in between two colours picked from a discrete palette:

function:   getIntermediateColourValue
parameters: c1(R,G,B), c2(R',G',B'), m: 0 <= m <= 1
return:     [R + m * (R' - R),
             G + m * (G' - G),
             B + m * (B' - B)]

Gimp[edit]

  • flatpak run org.gimp.GIMP

Commons[edit]

Template[edit]

log-polar mapping[edit]

To do[edit]

Mandelbrot[edit]

Mandelbrot set inversion, 4 different methods in one image by Arneauxtje

First, there's the transformation from the cardioid of the body of the set to a circle. This is done in c-space (a+ib) as follows:

rho=sqrt(a*a+b*b)-1/4
phi=arctan(b/a)
a-new=rho*(2*cos(phi)-cos(2*phi))/3
b-new=rho*(2*sin(phi)-sin(2*phi))/3

Then, there's the 4 different ways on how to get from c to 1/c, that group in 3 families:

  • addition: c -> c-c*t+t/c and t=0..1
  • multiplication: c -> c/(t*(c*c-1)+1) and t=0..1
  • exponentiation: c -> c^t and t=1..-1

The first 2 are pretty elementary to work out. The 3rd makes use of the fact that: c = a+ib = r*exp(i*phi) where r=sqrt(a*a+b*b) and phi=arctan(b/a) then c^t = r^t*exp(t*i*phi) = r^t*[cos(t*phi)+i*sin(t*phi)]

The top left is method 1, top right method 2, and the bottom 2 are variants of method 3. Hope this helps somewhat.

other images[edit]

other Julia[edit]

  • θ = 1/(10 + 1/(10 + · · ·)) Consider a polynomial P : C → C of degree d ≥ 2, with an irrationnally indifferent fixed point at the origin: P(0) = 0, P′ (0) = e 2iπθ, θ ∈ R \ Q. ( from On the linearization of degree three polynomials and Douady’s conjecture by Arnaud Ch´eritat (joint work with Xavier Buff)
  • (*Koch center 3 cycle Julia*)\[IndentingNewLine]f[z_]=(-0.187-0.421*I)z^3+(-2.332-0.239*I)z^2+(-0.285+2.879*I)z+1; Roger Lee BagulaSelf-Similarity and Fractals An example of a "Koch" Julia: I was looking for an image for my new music album and found this unique Julia and re-did the picture with different colors and higher resolution: https://www.wolframcloud.com/.../j_koch9p1example2000...
  • z^n + c*z where n=6, c=0.95 and R=0.2 https://geometricolor.wordpress.com/2013/10/28/coloring-the-julia-set/

cubic[edit]

  • A 4k cubic Julia by ‎Chris Thomasson‎ . Here is the formula: z = pow(z, 3) - (pow(-z, 2.00001) - 1.0008875); link
  • cubic
  • "Let c = (.387848...) + i(.6853...). The left picture shows the filled Julia set Kc of the cubic map z3 + c, covered by level 0 of the puzzle. The center of symmetry is at 0, the point where the rays converge is α and the other fixed points are marked by dotted arrows. In this example the rotation number around α is ρα = 25 and the ray angles are 5 121 7→ 15 121 7→ 45 121 7→ 14 121 7→ 42 121 7→ 5 121 . The right picture illustrates level 1 of the puzzle for the same map. "A New Partition Identity Coming from Complex Dynamics
  • Owen Maresh owen maresh(-0.4999999999999998 + 0.8660254037844387*I) - (0.2926009682749477 + 0.252068970984772*I)* z - (0.4916379276414715 + 0.2509264824918978*I)* z^2 + (0.2511839558093919 - 1.0778044459985288*I)* z^3

rational[edit]

Julia sets of rational maps ( not polynomials )

  • julia sets for z⁴+c/z and z²+c/z³ photoniclabs
  • McMullen Maps
  • The Julia sets, defined by the equation (\ref{julia}), can take all kinds of shapes, and a small change in $c$ can change the Julia set very greatly https://complex-analysis.com/content/julia_set.html

Christopher Williams[edit]

Family:

Examples:

  • Julia set of The most obvious feature is that it's full of holes! The fractal is homemorphic to (topologically the same as) the Sierpinski carpet
  • Julia set of z2 - 1 - 0.005z-2
  • f = z^2 - 0.01z^-2
  • f = z2 - 0.01z-2

Phoenix formula

  • z5 - 0.06iz-2

Robert L. Devaney[edit]

  • Singular perturbations of complex polynomials

Julia sets for fc(z) = z*z + c[edit]

const double Cx=-0.74543; const double Cy=0.11301;

-0.808 +0.174i;

-0.1 +0.651i; ( beween 1 and 3 period component of Mandelbrot set )

-0.294 +0.634i

spirals[edit]

  • on the parameter plane
    • part of M-set near Misiurewicz points
  • on the dynamic plane
    • Julia set near cut points
    • critical orbits
    • external rays landing on the parabolic or repelling perriodic points



 
 
 

In period 1 component of Mandelbrot set :

 

In period 2 component of Mandelbrot set :


table[edit]

Caption text
Period c r 1-r t p/q p/q - t image author address
1 0.37496784+i*0.21687214 0.99993612384259 0.000063879203489 0.1667830755386747 1/6 0.00011640887201 Cr6spiral.png 1
1 -0.749413589136570+0.015312826507689*i. 0.9995895293978963 0.00041047060211000001 0.4975611481254812 1/2 -0.00243885187451881 png 1
2 -0.757 + 0.027i 0.977981594918841 0.02201840508115904 0.01761164373863864 0/1 -0.01761164373863864 pauldelbrot 1 -(1/2)-> 2
2 -0.752 + 0.01i 0.9928061240745848 0.007193875925415205 0.006414063302849116 0/1 -0.006414063302849116 pauldelbrot 1 -(1/2)-> 2
10 -1.2029905319213867188 + 0.14635562896728515625 i 0.979333 0.02490599999999998 0.985187275828761422 0/1 -0.01481272417123857 marcm200 1 -(1/2)-> 2 -(2/5)-> 10
14 -1.2255649566650390625 0.1083774566650390625 0.951928 0.048072 0.992666114460366900 1/1 0.0073338855396331 marcm200 1 -(1/2)-> 2 -(3/7)-> 14
14 -1.2256811857223510742 +0.10814088582992553711 i 0.955071 0.044929 0.984062994677356362 1/1 0.01593700532264363 marcm200 1 -(1/2)-> 2 -(3/7)-> 14
14 -0.8422698974609375 -0.19476318359375 i 0.952171 0.04782900000000001 0.935491618649184731 1/1 0.06450838135081527 marcm200 1 -(1/2)-> 2 -(6/7)-> 14


pauldelbrot[edit]

"c=0.027*%i-0.757"

period =  1 
z= 0.01345178808414596*%i-0.5035840525848648 
r = |m(z)| = 1.007527366616821 
1-r = -0.007527366616821407 
t = turn(m(z))  =  0.4957496478171055 
p/q = 1/2 
p/q-t = -0.004250352182894435 
  
z= 1.503584052584865-0.01345178808414596*%i 
r = |m(z)| = 3.007288448945452 
1-r = -2.007288448945452 
t = turn(m(z))  =  0.9985761611087214 
p/q = 1/2 
p/q-t = 0.4985761611087214 
  
period =  2 
z= (-0.1022072682395012*%i)-0.3679154600985363 
r = |m(z)| = 0.977981594918841 
1-r = 0.02201840508115904 
t = turn(m(z))  =  0.01761164373863864 
p/q = 1/2 
p/q-t = -0.4823883562613613 
  
z= 0.1022072682395012*%i-0.6320845399014637 
r = |m(z)| = 0.9779815949188409 
1-r = 0.02201840508115915 
t = turn(m(z))  =  0.01761164373863864 
p/q = 1/2 
p/q-t = -0.4823883562613613 
  


c=0.01*%i-0.752"

period =  1 
z= 0.0049949453016411*%i-0.501011962705025 
r = |m(z)| = 1.002073722342039 
1-r = -0.00207372234203973 
t = turn(m(z))  =  0.498413323518715 
p/q = 0 
p/q-t = 0.498413323518715 
  
z= 1.501011962705025-0.0049949453016411*%i 
r = |m(z)| = 3.002040547136002 
1-r = -2.002040547136002 
t = turn(m(z))  =  0.9994703791038458 
p/q = 0 
p/q-t = 0.9994703791038458 
  
period =  2 
z= (-0.06402358560400053*%i)-0.4219037804142045 
r = |m(z)| = 0.9928061240745848 
1-r = 0.007193875925415205 
t = turn(m(z))  =  0.006414063302849116 
p/q = 0 
p/q-t = 0.006414063302849116 
  
z= 0.06402358560400053*%i-0.5780962195857955 
r = |m(z)| = 0.9928061240745848 
1-r = 0.007193875925415205 
t = turn(m(z))  =  0.006414063302849116 
p/q = 0 
p/q-t = 0.006414063302849116 
  
(%o296) "/home/a/Dokumenty/periodic/MaximaCAS/p1/p.mac"
(%i297) 

marcm200[edit]

the input point was -1.2029905319213867e+00 + +1.4635562896728516e-01 i
the point didn't escape after 10000 iterations
nearby hyperbolic components to the input point:

- a period 1 cardioid
  with nucleus at +0e+00 + +0e+00 i
  the component has size 1.00000e+00 and is pointing west
  the atom domain has size 0.00000e+00
  the atom domain coordinates of the input point are -nan + -nan i
  the atom domain coordinates in polar form are nan to the east
  the nucleus is 1.21186e+00 to the east of the input point
  the input point is exterior to this component at
  radius 1.41904e+00 and angle 0.486382891412633800 (in turns)
  the multiplier is -1.41385e+00 + +1.21263e-01 i
  a point in the attractor is -7.0694e-01 + +6.06308e-02 i
  external angles of this component are:
  .(0)
  .(1)

- a period 2 circle
  with nucleus at -1e+00 + +0e+00 i
  the component has size 5.00000e-01 and is pointing west
  the atom domain has size 1.00000e+00
  the atom domain coordinates of the input point are -0.20299 + +0.14636 i
  the atom domain coordinates in polar form are 0.25025 to the north-west
  the nucleus is 2.50250e-01 to the south-east of the input point
  the input point is exterior to this component at
  radius 1.00100e+00 and angle 0.400579159596292533 (in turns)
  the multiplier is -8.11962e-01 + +5.85423e-01 i
  a point in the attractor is +1.81557e-01 + -1.07368e-01 i

- a period 4 circle
  with nucleus at -1.310703e+00 + +3.761582e-37 i
  the component has size 1.17960e-01 and is pointing west
  the atom domain has size 2.34844e-01
  the atom domain coordinates of the input point are +0.507 + +0.53837 i
  the atom domain coordinates in polar form are 0.73952 to the north-east
  the nucleus is 1.81719e-01 to the south-west of the input point
  the input point is exterior to this component at
  radius 1.00200e+00 and angle 0.801158319192584956 (in turns)
  the multiplier is +3.16563e-01 + -9.50682e-01 i
  a point in the attractor is +1.815562e-01 + -1.073687e-01 i
  external angles of this component are:
  .(0110)
  .(1001)

- a period 10 circle
  with nucleus at -1.2103996e+00 + +1.5287483e-01 i
  the component has size 2.02739e-02 and is pointing north-west
  the atom domain has size 4.09884e-02
  the atom domain coordinates of the input point are +0.16767 + -0.13713 i
  the atom domain coordinates in polar form are 0.2166 to the south-east
  the nucleus is 9.86884e-03 to the north-west of the input point
  the input point is interior to this component at
  radius 9.79333e-01 and angle 0.985187275828761422 (in turns)
  the multiplier is +9.75094e-01 + -9.10160e-02 i
  a point in the attractor is +7.0332348e-02 + -8.243835e-02 i
  external angles of this component are:
  .(0110010110)
  .(0110011001)

the input point was -1.2255649566650391e+00 + +1.0837745666503906e-01 i
the point didn't escape after 10000 iterations
nearby hyperbolic components to the input point:

- a period 1 cardioid
  with nucleus at +0e+00 + +0e+00 i
  the component has size 1.00000e+00 and is pointing west
  the atom domain has size 0.00000e+00
  the atom domain coordinates of the input point are -nan + -nan i
  the atom domain coordinates in polar form are nan to the east
  the nucleus is 1.23035e+00 to the east of the input point
  the input point is exterior to this component at
  radius 1.43387e+00 and angle 0.490097175551864883 (in turns)
  the multiplier is -1.43109e+00 + +8.91595e-02 i
  a point in the attractor is -7.15546e-01 + +4.45805e-02 i
  external angles of this component are:
  .(0)
  .(1)

- a period 2 circle
  with nucleus at -1e+00 + +0e+00 i
  the component has size 5.00000e-01 and is pointing west
  the atom domain has size 1.00000e+00
  the atom domain coordinates of the input point are -0.22556 + +0.10838 i
  the atom domain coordinates in polar form are 0.25025 to the west-north-west
  the nucleus is 2.50250e-01 to the east-south-east of the input point
  the input point is exterior to this component at
  radius 1.00100e+00 and angle 0.428714049282459153 (in turns)
  the multiplier is -9.02260e-01 + +4.33510e-01 i
  a point in the attractor is +1.94019e-01 + -7.80792e-02 i

- a period 4 circle
  with nucleus at -1.310703e+00 + +0e+00 i
  the component has size 1.17960e-01 and is pointing west
  the atom domain has size 2.34844e-01
  the atom domain coordinates of the input point are +0.38418 + +0.4137 i
  the atom domain coordinates in polar form are 0.56457 to the north-east
  the nucleus is 1.37819e-01 to the south-west of the input point
  the input point is exterior to this component at
  radius 1.00200e+00 and angle 0.857428098564918195 (in turns)
  the multiplier is +6.26142e-01 + -7.82277e-01 i
  a point in the attractor is +1.940184e-01 + -7.80797e-02 i
  external angles of this component are:
  .(0110)
  .(1001)

- a period 14 circle
  with nucleus at -1.2299714e+00 + +1.1067143e-01 i
  the component has size 1.06543e-02 and is pointing west-north-west
  the atom domain has size 1.95731e-02
  the atom domain coordinates of the input point are +0.16376 + -0.15414 i
  the atom domain coordinates in polar form are 0.22489 to the south-east
  the nucleus is 4.96796e-03 to the west-north-west of the input point
  the input point is interior to this component at
  radius 9.51928e-01 and angle 0.992666114460366900 (in turns)
  the multiplier is +9.50917e-01 + -4.38495e-02 i
  a point in the attractor is +7.5747371e-02 + -5.129233e-02 i
  external angles of this component are:
  .(01100110010110)
  .(01100110011001)
the input point was -1.2256811857223511e+00 + +1.0814088582992554e-01 i
the point didn't escape after 10000 iterations
nearby hyperbolic components to the input point:

- a period 1 cardioid
  with nucleus at +0e+00 + +0e+00 i
  the component has size 1.00000e+00 and is pointing west
  the atom domain has size 0.00000e+00
  the atom domain coordinates of the input point are -nan + -nan i
  the atom domain coordinates in polar form are nan to the east
  the nucleus is 1.23044e+00 to the east of the input point
  the input point is exterior to this component at
  radius 1.43394e+00 and angle 0.490119703062896594 (in turns)
  the multiplier is -1.43118e+00 + +8.89616e-02 i
  a point in the attractor is -7.15576e-01 + +4.44813e-02 i
  external angles of this component are:
  .(0)
  .(1)

- a period 2 circle
  with nucleus at -1e+00 + +0e+00 i
  the component has size 5.00000e-01 and is pointing west
  the atom domain has size 1.00000e+00
  the atom domain coordinates of the input point are -0.22568 + +0.10814 i
  the atom domain coordinates in polar form are 0.25025 to the west-north-west
  the nucleus is 2.50253e-01 to the east-south-east of the input point
  the input point is exterior to this component at
  radius 1.00101e+00 and angle 0.428881674271762436 (in turns)
  the multiplier is -9.02725e-01 + +4.32564e-01 i
  a point in the attractor is +1.9408e-01 + -7.79018e-02 i

- a period 4 circle
  with nucleus at -1.310703e+00 + +0e+00 i
  the component has size 1.17960e-01 and is pointing west
  the atom domain has size 2.34844e-01
  the atom domain coordinates of the input point are +0.38355 + +0.41286 i
  the atom domain coordinates in polar form are 0.56353 to the north-east
  the nucleus is 1.37561e-01 to the south-west of the input point
  the input point is exterior to this component at
  radius 1.00202e+00 and angle 0.857763348543524873 (in turns)
  the multiplier is +6.27801e-01 + -7.80972e-01 i
  a point in the attractor is +1.940823e-01 + -7.790208e-02 i
  external angles of this component are:
  .(0110)
  .(1001)

- a period 14 circle
  with nucleus at -1.2299714e+00 + +1.1067143e-01 i
  the component has size 1.06543e-02 and is pointing west-north-west
  the atom domain has size 1.95731e-02
  the atom domain coordinates of the input point are +0.15716 + -0.16242 i
  the atom domain coordinates in polar form are 0.22601 to the south-east
  the nucleus is 4.98108e-03 to the west-north-west of the input point
  the input point is interior to this component at
  radius 9.55071e-01 and angle 0.984062994677356362 (in turns)
  the multiplier is +9.50287e-01 + -9.54765e-02 i
  a point in the attractor is +6.2976569e-02 + -5.7543144e-02 i
  external angles of this component are:
  .(01100110010110)
  .(01100110011001)
the input point was -8.422698974609375e-01 + -1.9476318359375e-01 i
the point didn't escape after 10000 iterations
nearby hyperbolic components to the input point:

- a period 1 cardioid
  with nucleus at +0e+00 + +0e+00 i
  the component has size 1.00000e+00 and is pointing west
  the atom domain has size 0.00000e+00
  the atom domain coordinates of the input point are -nan + -nan i
  the atom domain coordinates in polar form are nan to the east
  the nucleus is 8.64495e-01 to the east-north-east of the input point
  the input point is exterior to this component at
  radius 1.11403e+00 and angle 0.526643305764455283 (in turns)
  the multiplier is -1.09846e+00 + -1.85625e-01 i
  a point in the attractor is -5.49225e-01 + -9.28116e-02 i
  external angles of this component are:
  .(0)
  .(1)

- a period 2 circle
  with nucleus at -1e+00 + +0e+00 i
  the component has size 5.00000e-01 and is pointing west
  the atom domain has size 1.00000e+00
  the atom domain coordinates of the input point are +0.15773 + -0.19476 i
  the atom domain coordinates in polar form are 0.25062 to the south-east
  the nucleus is 2.50622e-01 to the north-west of the input point
  the input point is exterior to this component at
  radius 1.00249e+00 and angle 0.858340235783291439 (in turns)
  the multiplier is +6.30920e-01 + -7.79053e-01 i
  a point in the attractor is -1.0771e-01 + +2.48238e-01 i

- a period 14 circle
  with nucleus at -8.4076071e-01 + -1.9927227e-01 i
  the component has size 1.01164e-02 and is pointing south-east
  the atom domain has size 1.66560e-02
  the atom domain coordinates of the input point are +0.13324 + -0.2159 i
  the atom domain coordinates in polar form are 0.25371 to the south-south-east
  the nucleus is 4.75495e-03 to the south-south-east of the input point
  the input point is interior to this component at
  radius 9.52171e-01 and angle 0.935491618649184731 (in turns)
  the multiplier is +8.75023e-01 + -3.75452e-01 i
  a point in the attractor is +4.338561e-02 + +7.777828e-02 i
  external angles of this component are:
  .(10101010100110)
  .(10101010101001)

basilica[edit]

  • San Marco Fractal = Basilica : c = - 3/4

perturbated[edit]

disconnected[edit]

near c = -0.750357820200574 +0.047756163825227 i

3 petals[edit]

Siegel Disk[edit]

Julia set = Jordan curve Irrational recurrent cycles

  • 0.59...+i0.43...
  • 0.33...+i0.07...
  • C= -0.408792866 -0.577405 i
  • c=-0.390541-0.586788i

Other[edit]

Feigenbaum: C= -1.4011552 +0.0 i

Tower: C= -1 + 0.0 i

Cauliflower: C= 0.25 +0.0 i


Dendrite[edit]

Critical point eventually periodic 0 > -2 > 2 (fixed).

C= i

c^3 + 2c^2 +2c +2 =0


3[edit]

The core entropy for polynomials of higher degree Yan Hong Gao, Giulio Tiozzo The Julia set of fc(z) = z → z3 + 0.22036 + 1.18612i

To show the non-uniqueness, let us consider the following example, which comes from [Ga]. We consider the postcritically finite polynomial fc(z) = z3 + c with c ≈ 0.22036 + 1.18612i. The critical value c receives two rays with arguments 11/72 and 17/72. Then, Θ := { Θ1(0) := {11/216, 83/216} , Θ2(0) := {89/216, 161/21

Other[edit]

Circle: C= 0.0 +0.0 i

Segment: C= -2 +0.0 i

centers[edit]

  • c = -0.748490484405062 +0.048290910555737 i period = 65 ( 1 -? - > 65 )
  • by ‎Chris Thomasson‎
    • (0.355534, -0.337292) it is a center of period 85 componnet. Adress 1->5 -> 85,
    • 29 cycle power of two Julia set at point: (-0.742466, -0.107902) address 1 -> 29
    • 38-cycle power of 3 Julia at point (0.388823, -0.000381453)
  • c = -0.051707765779845 +0.683880135777732 i period = 273, 1 -(1/3)-> 3 -(1/7)-> 21 -(1/13)-> 273 https://www.math.stonybrook.edu/~jack/tune-b.pdf
  • https://arxiv.org/pdf/math/9411238.pdf see Figure.2
    • 1- (1/3) → 3 -(2/3) → 7
    • 1 - (1/2) -> 2 - (1/2) → 4 -(1/3) → 7
    • 1-(1/3) → 3- (1/2) → 4
    • 1-(1/3) → 3 - (1/2) → 5-(1/2) → 6
    • 1-(1/3) → 3-(1/2) → 5-(1/2) → 7
    • 1-(1/3) → 3-(1/3) → 7
    • 1-(3/4)-> 4 -(?/5)-> 20 : c = 0.300078079301992 -0.489531524188048 i period = 20
  • http://wrap.warwick.ac.uk/35776/1/WRAP_THESIS_Sharland_2010.pdf

minibrot[edit]

  • c = 0.284912968784722 +0.484816779093857 i period = 84


Superattracting per 3 (up to complex conjugate)[edit]

C= -1.75488 (airplane)

C= -0.122561 + 0.744862 i (rabbit) Douady's Rabbit Rabbit: C= -0.122561 +0.744862 i = ( -1/8+3/4 i ??? ) whose critical point 0 is on a periodic orbit of length 3


Superattracting per 4 (up to complex conjugate)[edit]

C= -1.9408

C= -1.3107

C= -1.62541

C= -0.15652 +1.03225 i

C= 0.282271 +0.530061 i


Kokopelli[edit]

  • p = γM (3/15)
  • p(z) = z^2 0.156 + 1.302*i
  • The angle 3/15 or p0011 has preperiod = 0 and period = 4.
  • The conjugate angle is 4/15 or p0100 .
  • The kneading sequence is AAB* and the internal address is 1-3-4 .
  • The corresponding parameter rays are landing at the root of a primitive component of period 4.
  • c = -0.156520166833755 +1.032247108922832 i period = 4


Superattracting per 5 (up to complex conjugate)[edit]

C= -1.98542

C= -1.86078

C= -1.62541

C= -1.25637 +0.380321 i

C= -0.50434 +0.562766 i

C= -0.198042 +1.10027 i

C= -0.0442124 +0.986581 i

C= 0.359259 +0.642514 i

C= 0.379514 +0.334932 i

A superattracting per 15[edit]

C= -0.0384261 +0.985494 i

dense[edit]

Vivid-Thick-Spiral[edit]


VividThickSpiral { fractal:

 title="Vivid Thick Spiral" width=800 height=600 layers=1
 credits="Ingvar Kullberg;1/7/2014;Frederik Slijkerman;7/23/2002"

layer:

 caption="Background" opacity=100 method=multipass

mapping:

 center=-0.745655283381030620841/0.07611785523064665900025
 magn=3.7328517E10

formula:

 maxiter=1000000 percheck=off filename="Standard.ufm"
 entry="Mandelbrot" p_start=0/0 p_power=2/0 p_bailout=100

inside:

 transfer=none

outside:

 density=0.1 transfer=arctan filename="Standard.ucl" entry="Basic"
 p_type=Iteration

gradient:

 smooth=yes rotation=93 index=151 color=16580604 index=217
 color=1909029 index=227 color=2951679 index=248 color=6682867
 index=262 color=223 index=291 color=255 index=-29 color=55539

opacity:

 smooth=no index=0 opacity=255

}

Pink-Labyrinth[edit]

PinkLabyrinth { fractal:

 title="Pink Labyrinth" width=800 height=600 layers=1
 credits="Ingvar Kullberg;1/7/2014;Frederik Slijkerman;7/23/2002"

layer:

 caption="Background" opacity=100 method=multipass

mapping:

 center=-0.745655283616919391525/0.0761178553836136017335
 magn=6.6880259E9

formula:

 maxiter=1000000 filename="Standard.ufm" entry="Mandelbrot"
 p_start=0/0 p_power=2/0 p_bailout=100

inside:

 transfer=none

outside:

 density=0.25 transfer=arctan filename="Standard.ucl" entry="Basic"
 p_type=Iteration

gradient:

 smooth=yes rotation=74 index=132 color=16580604 index=198
 color=1909029 index=208 color=2951679 index=229 color=6682867
 index=243 color=223 index=272 color=255 index=-48 color=55539

opacity:

 smooth=no index=0 opacity=255

}

IMAGE DETAILS


Density near the cardoid 3[edit]

https://www.deviantart.com/dinkydauset/art/Density-near-the-cardoid-3-729541183

  • Magnification:
    • 2^35.769
    • 5.8552024369543422761426995117521 E10
  • Coordinates:
    • Re = 0.360999615968828800
    • Im = -0.121129382033034400


Density near the cardoid 3 by DinkydauSet[edit]

https://fractalforums.org/image-threads/25/mandelbrot-set-various-structures/716/;topicseen


Mandelbrot set

Again a location that's not deep but super dense.

Magnification: 2^35.769 5.8552024369543422761426995117521 E10

Coordinates: Re = 0.360999615968828800 Im = -0.121129382033034400

XaoS coordinates

(maxiter 50000) (view -0.775225602760841 -0.136878655029377 7.14008235131944E-11 7.14008235674045E-11)

https://arxiv.org/pdf/1703.01206.pdf "Limbs 8/21, 21/55, 55/144, 144/377, . . . scale geometrically fast on the right side of the (anti-)golden Siegel parameter, while limbs 5/13, 13/34, 34/89, 89/233, . . . scale geometrically fast on the left side. The bottom picture is a zoom of the top picture."

a[edit]

https://plus.google.com/u/0/photos/115452635610736407329/albums/6124078542095960129/6124078748270945650 frond tail Misiurewicz point of the period-27 bulb of the quintic Mandelbrot set (I don't have a number ATM, but you can find that)

Machine-readable_data[edit]

SVG[edit]

<?xml version="1.0" encoding="utf-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">


Links :

Bezier curve[edit]

ps[edit]

"Obrazy w indywidualnym wkładzie, mam z samodzielnie napisanymi programami PASCAL (FREEPASCAL) i / lub XFIG (program do rysowania pod LINUX) początkowo tworzone jako pliki EPS. Niestety bezpośrednia integracja plików EPS z Wikipedią nie jest możliwa. Przydatna jest konwersja plików EPS na pliki XFIG za pomocą PSTOEDIT. Konwersja plików EPS na pliki SVG jest możliwa dzięki INKSCAPE, a także eksportowi plików xfig do plików SVG. Jednak nie znalazłem zamiennika dla etykiety LATEX, włączając ją do pliku LATEX w środowisku rysunkowym z plikiem psfrag. Także dla licznych możliwości manipulowania krzywymi za pomocą xfig wiem w inkscape (wciąż) brak odpowiednika. Z plików PS tworzę pliki SVG z ps2pdf i pdf2svg i używam programu inkscape do dostosowania stron (marginesów) do rysunków." de:Benutzer:Ag2gaeh

Help[edit]

differences between :

<gallery> </gallery>
{{SUL Box|en|wikt}}


[[1]]

compare with[edit]


==Compare with==

<gallery caption="Sample gallery" widths="100px" heights="100px" perrow="6">

</gallery>

</nowiki>

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metadata[edit]

syntaxhighlight[edit]

== c source code==
<syntaxhighlight lang="c">
</syntaxhighlight>

== bash source code==
<syntaxhighlight lang="bash">
</syntaxhighlight>


==text output==
<pre>

references[edit]

  1. educativesite : 2 d-graphics-pipeline-block-diagram
  2. Linux and High Dynamic Range (HDR) Display by Andy Ritger ( 2016)
  3. fractal_ken An "escape time" fractal generated by homemade software using recurrence relation z(n) = z(n - 1)^2 + 0.3305 + 0.06i

GeSHi[edit]

description:

<syntaxhighlight lang="c" enclose="none">
g;
a=2;
</syntaxhighlight>


source templetate[edit]

deprecated:

<syntaxhighlight lang="gnuplot">ssssssssssssss</syntaxhighlight>

see also[edit]


wikitable collapsible collapsed[edit]



navbox collapsible collapsed = Template:Source_code[edit]

w:Template:Source_code

prettytable[edit]

Icon Mathematical Plot.svg      Mathematical Function Plot
Description Function displaying a cusp at (0,1)
Equation
Co-ordinate System Cartesian
X Range -4 .. 4
Y Range -0 .. 3
Derivative
 
Points of Interest in this Range
Minima
Cusps
Derivatives at Cusp ,

Language[edit]

references[edit]