2 changed files with 809 additions and 0 deletions
809
∣❁∣✤✻ᕭᕮᗩߦറߦᗩᕭᕮ✻✤∣❁∣/◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇⠀ ⠀◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇/ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN⠀ ⠀ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN/ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄✣ⵙИN⩇ИNⵙ✣𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ/⅃MX.𐫰⊚ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ⊚𐫰.XML
809
∣❁∣✤✻ᕭᕮᗩߦറߦᗩᕭᕮ✻✤∣❁∣/◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇⠀ ⠀◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇/ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN⠀ ⠀ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN/ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄✣ⵙИN⩇ИNⵙ✣𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ/⅃MX.𐫰⊚ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ⊚𐫰.XML
@ -0,0 +1,809 @@ |
|||
<?xml version="1.0" encoding="utf-8" standalone="yes"?> |
|||
<Fractal BackgroundVisible="True" BackColor="FFFFFF00" BorderWidth="0" StripBorder="True" PixelSize="0.00548779710473845" Pixels.X="729" Pixels.Y="729" ClassicProcessing="None" OrbitTrapProcessing="ActivateControllers" SolidGuessing="None"> |
|||
<FractalNotes><![CDATA[]]></FractalNotes> |
|||
<FractalEquation Id="adb85431-618d-491f-b8c5-08555b119814" Title="Pixel"> |
|||
<Instructions><![CDATA[ |
|||
comment: |
|||
|
|||
This equation can be used when no equation is necessary. |
|||
By setting the MinDwell/MaxDwell to 1 below, we limit |
|||
the iteration to a single step for best performance. |
|||
|
|||
global: |
|||
|
|||
FSK.OverrideValue("MinDwell", 1) |
|||
FSK.OverrideValue("MaxDwell", 1) |
|||
|
|||
iterate: |
|||
|
|||
z = c |
|||
]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</FractalEquation> |
|||
<TransformationArray> |
|||
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</Transformation> |
|||
</TransformationArray> |
|||
<TransformationArray> |
|||
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</Transformation> |
|||
</TransformationArray> |
|||
<AlternateValueInfo AlternateValueNNormalize="True" AlternateValueNInvert="True" /> |
|||
<AlternateValueInfo /> |
|||
<OrbitTrapInfo> |
|||
<OrbitTrapArray TrapIndexMapping="CombinedIndex" TrapDeltaMapping="TrapDelta" GroupByTrap="False" BlendValues="False"> |
|||
<OrbitTransform /> |
|||
<OrbitTransform /> |
|||
<TransformationArray> |
|||
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</Transformation> |
|||
</TransformationArray> |
|||
<TransformationArray> |
|||
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</Transformation> |
|||
</TransformationArray> |
|||
<SymmetryTransformation Id="8301dc6c-2273-4fb9-ada8-2ded2833031f" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</SymmetryTransformation> |
|||
<OrbitTrapItem TrapId="4"> |
|||
<OrbitTrap Id="4e4b2e73-dc52-4107-bb98-f9abb8745748" Title="Unit Circle Group"> |
|||
<Instructions><![CDATA[ |
|||
comment: |
|||
|
|||
trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring) |
|||
trappedPoint.Delta is the level: 0 - Steps-1 |
|||
|
|||
See the paper: |
|||
"Evolution of Math into Art via Mobius Transformations" |
|||
by Anne M. Burns, Department of Mathematics, |
|||
Long Island University. |
|||
http://myweb.cwpost.liu.edu/aburns/ |
|||
|
|||
Also, see pages 88-89 in the book: |
|||
"Indra's Pearls, The Vision of Felix Klein" |
|||
by David Mumford, Caroline Series, David Wright. |
|||
http://klein.math.okstate.edu/IndrasPearls/ |
|||
|
|||
global: |
|||
|
|||
Complex ShowCenter[] = LC1,LC2,LC3,LC4,LC5,LC6,LC7,LC8,LC9,LC10,LC11,LC12,LC13,LC14,LC15,LC16 |
|||
Complex ShowRing[] = LR1,LR2,LR3,LR4,LR5,LR6,LR7,LR8,LR9,LR10,LR11,LR12,LR13,LR14,LR15,LR16 |
|||
AbsV = Sqrt(AbsU^2 - 1) |
|||
u = AbsU * Cis(DegreeToRadian(ArgU)) |
|||
v = AbsV * Cis(DegreeToRadian(ArgV)) |
|||
Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u)) |
|||
Mobius m[N+1] |
|||
' |
|||
' Given N, find radius R such that N circles with radius R can be |
|||
' placed along the inside of the unit circle, each tangent to the |
|||
' unit circle and each of its two adjacent neighbors. The centers |
|||
' of all circles are a distance of 1-R from the origin. The centers |
|||
' of all circles form a regular polygon P with N sides and each edge |
|||
' has length = 2*(1-R)*Sin(pi/N). Since all N circles are pairwise |
|||
' tangent, the edge of P must equal 2*R, so 2*R = 2*(1-R)*Sin(pi/N). |
|||
' Solving for R yields R = 1/(1+1/Sin(pi/N)). |
|||
' |
|||
r = 1/(1+1/Sin(Math.PI/N)) |
|||
|
|||
step = 2*Math.PI/N |
|||
ang = IIf(Shift, step/2, 0) |
|||
' |
|||
' Generate the Mobius transformation that transforms the |
|||
' unit circle into the circle in the center of the ring. |
|||
' |
|||
m[0] = Mobius(1-2*r, 0, 0, 1) |
|||
' |
|||
' Generate the set of N Mobius transformations the |
|||
' transform the unit circle into the i'th circle in the |
|||
' ring, where i = 1 to N. |
|||
' |
|||
for (i = 1, i <= N, i += 1) { |
|||
rotate = Cis(ang) |
|||
|
|||
m[i] = Mobius.Multiply( \ |
|||
Mobius(r*rotate, (1-r)*rotate, 0, 1), \ |
|||
UnitCircleGroup \ |
|||
) |
|||
ang += step |
|||
} |
|||
' |
|||
' Assign Total = the total number of circles. |
|||
' |
|||
const Complex Total = 0 |
|||
count = N+1 |
|||
|
|||
for (i = 0, i < Steps, i += 1) { |
|||
Total += count |
|||
count *= N+1 |
|||
} |
|||
const Circle c[Total] |
|||
const Complex index[Total] |
|||
const Complex level[Total] |
|||
Circle UnitCircle = CircleC(0, 1) |
|||
' |
|||
' Generate the base ring and center circles. |
|||
' |
|||
for (i = 0, i <= N, i += 1) { |
|||
c[i] = Mobius.TransformCircle(m[i], UnitCircle) |
|||
index[i] = i |
|||
level[i] = 0 |
|||
} |
|||
count = N+1 |
|||
max = 0 |
|||
' |
|||
' Generate the remaining circles. |
|||
' |
|||
if (Steps > 1) { |
|||
for (i = 1, i < Steps, i += 1) { |
|||
min = max |
|||
max = count |
|||
|
|||
for (j = min, j < max, j += 1) { |
|||
for (k = 0, k < N+1, k += 1) { |
|||
c[count] = Mobius.TransformCircle(m[k], c[j]) |
|||
' |
|||
' Skip circles that are too small. |
|||
' |
|||
if (c[count].Radius >= RadiusMin) { |
|||
index[count] = index[j] |
|||
level[count] = i |
|||
count += 1 |
|||
} |
|||
} |
|||
} |
|||
} |
|||
} |
|||
' |
|||
' Reset Total in case you skipped circles that were too small. |
|||
' |
|||
Total = count |
|||
|
|||
CurveTrap.Initialize( \ |
|||
Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \ |
|||
) |
|||
' |
|||
' Add the circles to the trap based on user criteria. |
|||
' |
|||
for (i = 0, i < Total, i += 1) { |
|||
lev = level[i] |
|||
idx = index[i] |
|||
' |
|||
' Note: idx=N for center circles. |
|||
' |
|||
if (idx = 0) { |
|||
if (ShowCenter[lev]) { |
|||
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) |
|||
} |
|||
} else { |
|||
if (ShowRing[lev]) { |
|||
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) |
|||
} |
|||
} |
|||
} |
|||
|
|||
trap: |
|||
|
|||
trappedPoint = CurveTrap.Apply(z) |
|||
|
|||
properties: |
|||
|
|||
divider { |
|||
caption = "General Options" |
|||
} |
|||
option Center { |
|||
type = Complex |
|||
caption = "Center" |
|||
details = "Center of trap" |
|||
default = 0 |
|||
} |
|||
option Angle { |
|||
type = Float |
|||
caption = "Angle" |
|||
details = "Angle of rotation" |
|||
default = 0 |
|||
range = [-360,360] |
|||
} |
|||
option Scale { |
|||
type = Float |
|||
caption = "Scale" |
|||
details = "Scale factor applied to trap" |
|||
range = (0,) |
|||
default = 2 |
|||
} |
|||
option Solid { |
|||
type = Boolean |
|||
caption = "Solid" |
|||
details = "Check to create solid trap" |
|||
default = False |
|||
} |
|||
option AlternateAngle { |
|||
type = Boolean |
|||
caption = "Alternate Angle" |
|||
details = "Use alternate angle calculation" |
|||
default = False |
|||
} |
|||
option LineWidth { |
|||
type = Float |
|||
caption = "Line Width" |
|||
details = "Extent of trap on either side of curve (> 0)" |
|||
range = (0,) |
|||
default = 0.00411522633744855967078189300413 |
|||
enabled = ~Solid |
|||
} |
|||
divider { |
|||
caption = "U/V Controls" |
|||
} |
|||
option AbsU { |
|||
type = Float |
|||
caption = "Abs(U)" |
|||
details = "Magnitude of U (1-2)" |
|||
default = 1.1 |
|||
range = [1,2] |
|||
} |
|||
option ArgU { |
|||
type = Float |
|||
caption = "Arg(U)" |
|||
details = "Angle of U" |
|||
default = 0 |
|||
range = [-360,360] |
|||
} |
|||
option ArgV { |
|||
type = Float |
|||
caption = "Arg(V)" |
|||
details = "Angle of V" |
|||
default = 180 |
|||
range = [-360,360] |
|||
} |
|||
divider { |
|||
caption = "Circle Controls" |
|||
} |
|||
option N { |
|||
type = IntegerEnum(3,12) |
|||
caption = "N" |
|||
details = "Number of base circles" |
|||
default = 4 |
|||
} |
|||
option Steps { |
|||
type = IntegerEnum(1,16) |
|||
caption = "Steps" |
|||
details = "Number of inversion steps" |
|||
default = 8 |
|||
} |
|||
option Shift { |
|||
type = Boolean |
|||
caption = "Shift" |
|||
details = "Check to rotate initial chain by pi/N" |
|||
default = False |
|||
} |
|||
option RadiusMin { |
|||
type = Float |
|||
caption = "Radius Min" |
|||
details = "Minimum acceptable circle radius" |
|||
default = 0 |
|||
range = [0,) |
|||
} |
|||
#define ShowLevel(Index) |
|||
|
|||
divider { |
|||
caption = "Level #Index# Options" |
|||
} |
|||
option LR#Index# { |
|||
type = Boolean |
|||
caption = "Show Ring" |
|||
details = "Show ring of circles at level #Index#" |
|||
default = True |
|||
enabled = Steps >= #Index# |
|||
} |
|||
option LC#Index# { |
|||
type = Boolean |
|||
caption = "Show Center" |
|||
details = "Show center circle at level #Index#" |
|||
default = True |
|||
enabled = Steps >= #Index# |
|||
} |
|||
#end |
|||
|
|||
#include ShowLevel("1") |
|||
#include ShowLevel("2") |
|||
#include ShowLevel("3") |
|||
#include ShowLevel("4") |
|||
#include ShowLevel("5") |
|||
#include ShowLevel("6") |
|||
#include ShowLevel("7") |
|||
#include ShowLevel("8") |
|||
#include ShowLevel("9") |
|||
#include ShowLevel("10") |
|||
#include ShowLevel("11") |
|||
#include ShowLevel("12") |
|||
#include ShowLevel("13") |
|||
#include ShowLevel("14") |
|||
#include ShowLevel("15") |
|||
#include ShowLevel("16")]]></Instructions> |
|||
<PropertyValueOverrides> |
|||
<Option Name="Solid" Type="BooleanOption" Value="True" /> |
|||
<Option Name="ArgU" Type="FloatOption" Value="180" /> |
|||
<Option Name="ArgV" Type="FloatOption" Value="0" /> |
|||
<Option Name="LR1" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR2" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR3" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR4" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR5" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR6" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR7" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR8" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR9" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR10" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR11" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LR12" Type="BooleanOption" Value="False" /> |
|||
</PropertyValueOverrides> |
|||
</OrbitTrap> |
|||
</OrbitTrapItem> |
|||
<OrbitTrapItem TrapId="3"> |
|||
<OrbitTrap Id="4e4b2e73-dc52-4107-bb98-f9abb8745748" Title="Unit Circle Group"> |
|||
<Instructions><![CDATA[Φ |
|||
comment: |
|||
|
|||
trappedPoint.Index is the base circle index: 0 (center), 1-N (in ring) |
|||
trappedPoint.Delta is the level: 0 - Steps-1 |
|||
|
|||
See the paper: |
|||
"Evolution of Math into Art via Mobius Transformations" |
|||
by Anne M. Burns, Department of Mathematics, |
|||
Long Island University. |
|||
http://myweb.cwpost.liu.edu/aburns/ |
|||
|
|||
Also, see pages 88-89 in the book: |
|||
"Indra's Pearls, The Vision of Felix Klein" |
|||
by David Mumford, Caroline Series, David Wright. |
|||
http://klein.math.okstate.edu/IndrasPearls/ |
|||
|
|||
global: |
|||
|
|||
Complex ShowCenter[] = LC1, LC2, LC3, LC4, LC5, LC6 |
|||
Complex ShowRing[] = LR1, LR2, LR3, LR4, LR5, LR6 |
|||
AbsV = Sqrt(AbsU^2 - 1) |
|||
u = AbsU * Cis(DegreeToRadian(ArgU)) |
|||
v = AbsV * Cis(DegreeToRadian(ArgV)) |
|||
Mobius UnitCircleGroup = Mobius(u, v, Conj(v), Conj(u)) |
|||
Mobius m[N+1] |
|||
' |
|||
' Given N, find radius R such that N circles with radius R can be |
|||
' placed along the inside of the unit circle, each tangent to the |
|||
' unit circle and each of its two adjacent neighbors. The centers |
|||
' of all circles are a distance of 1-R from the origin. The centers |
|||
' of all circles form a regular polygon P with N sides and each edge |
|||
' has length = 2*(1-R)*Sin(pi/N). Since all N circles are pairwise |
|||
' tangent, the edge of P must equal 2*R, so 2*R = 2*(1-R)*Sin(pi/N). |
|||
' Solving for R yields R = 1/(1+1/Sin(pi/N)). |
|||
' |
|||
r = 1/(1+1/Sin(Math.PI/N)) |
|||
|
|||
step = 2*Math.PI/N |
|||
ang = IIf(Shift, step/2, 0) |
|||
' |
|||
' Generate the Mobius transformation that transforms the |
|||
' unit circle into the circle in the center of the ring. |
|||
' |
|||
m[0] = Mobius(1-2*r, 0, 0, 1) |
|||
' |
|||
' Generate the set of N Mobius transformations the |
|||
' transform the unit circle into the i'th circle in the |
|||
' ring, where i = 1 to N. |
|||
' |
|||
for (i = 1, i <= N, i += 1) { |
|||
rotate = Cis(ang) |
|||
|
|||
m[i] = Mobius.Multiply( \ |
|||
Mobius(r*rotate, (1-r)*rotate, 0, 1), \ |
|||
UnitCircleGroup \ |
|||
) |
|||
ang += step |
|||
} |
|||
' |
|||
' Assign Total = the total number of circles. |
|||
' |
|||
const Complex Total = 0 |
|||
count = N+1 |
|||
|
|||
for (i = 0, i < Steps, i += 1) { |
|||
Total += count |
|||
count *= N+1 |
|||
} |
|||
const Circle c[Total] |
|||
const Complex index[Total] |
|||
const Complex level[Total] |
|||
Circle UnitCircle = CircleC(0, 1) |
|||
' |
|||
' Generate the base ring and center circles. |
|||
' |
|||
for (i = 0, i <= N, i += 1) { |
|||
c[i] = Mobius.TransformCircle(m[i], UnitCircle) |
|||
index[i] = i |
|||
level[i] = 0 |
|||
} |
|||
count = N+1 |
|||
max = 0 |
|||
' |
|||
' Generate the remaining circles. |
|||
' |
|||
if (Steps > 1) { |
|||
for (i = 1, i < Steps, i += 1) { |
|||
min = max |
|||
max = count |
|||
|
|||
for (j = min, j < max, j += 1) { |
|||
for (k = 0, k < N+1, k += 1) { |
|||
c[count] = Mobius.TransformCircle(m[k], c[j]) |
|||
' |
|||
' Skip circles that are too small. |
|||
' |
|||
if (c[count].Radius >= RadiusMin) { |
|||
index[count] = index[j] |
|||
level[count] = i |
|||
count += 1 |
|||
} |
|||
} |
|||
} |
|||
} |
|||
} |
|||
' |
|||
' Reset Total in case you skipped circles that were too small. |
|||
' |
|||
Total = count |
|||
|
|||
CurveTrap.Initialize( \ |
|||
Center, DegreeToRadian(Angle), Scale, AlternateAngle, 6, False, LineWidth \ |
|||
) |
|||
' |
|||
' Add the circles to the trap based on user criteria. |
|||
' |
|||
for (i = 0, i < Total, i += 1) { |
|||
lev = level[i] |
|||
idx = index[i] |
|||
' |
|||
' Note: idx=N for center circles. |
|||
' |
|||
if (idx = 0) { |
|||
if (ShowCenter[lev]) { |
|||
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) |
|||
} |
|||
} else { |
|||
if (ShowRing[lev]) { |
|||
CurveTrap.AddCircle2(c[i], Solid, IIf(Solid, lev, 0), idx, lev) |
|||
} |
|||
} |
|||
} |
|||
|
|||
trap: |
|||
|
|||
trappedPoint = CurveTrap.Apply(z) |
|||
|
|||
properties: |
|||
|
|||
divider { |
|||
caption = "General Options" |
|||
} |
|||
option Center { |
|||
type = Complex |
|||
caption = "Center" |
|||
details = "Center of trap" |
|||
default = 0 |
|||
} |
|||
option Angle { |
|||
type = Float |
|||
caption = "Angle" |
|||
details = "Angle of rotation" |
|||
default = 0 |
|||
range = [-360,360] |
|||
} |
|||
option Scale { |
|||
type = Float |
|||
caption = "Scale" |
|||
details = "Scale factor applied to trap" |
|||
range = (0,) |
|||
default = 2 |
|||
} |
|||
option Solid { |
|||
type = Boolean |
|||
caption = "Solid" |
|||
details = "Check to create solid trap" |
|||
default = False |
|||
} |
|||
option AlternateAngle { |
|||
type = Boolean |
|||
caption = "Alternate Angle" |
|||
details = "Use alternate angle calculation" |
|||
default = False |
|||
} |
|||
option LineWidth { |
|||
type = Float |
|||
caption = "Line Width" |
|||
details = "Extent of trap on either side of curve (> 0)" |
|||
range = (0,) |
|||
default = 0.00411522633744855967078189300413 |
|||
enabled = ~Solid |
|||
} |
|||
divider { |
|||
caption = "U/V Controls" |
|||
} |
|||
option AbsU { |
|||
type = Float |
|||
caption = "Abs(U)" |
|||
details = "Magnitude of U (1-2)" |
|||
default = 1.1 |
|||
range = [1,2] |
|||
} |
|||
option ArgU { |
|||
type = Float |
|||
caption = "Arg(U)" |
|||
details = "Angle of U" |
|||
default = 0 |
|||
range = [-360,360] |
|||
} |
|||
option ArgV { |
|||
type = Float |
|||
caption = "Arg(V)" |
|||
details = "Angle of V" |
|||
default = 180 |
|||
range = [-360,360] |
|||
} |
|||
divider { |
|||
caption = "Circle Controls" |
|||
} |
|||
option N { |
|||
type = IntegerEnum(3,16) |
|||
caption = "N" |
|||
details = "Number of base circles" |
|||
default = 4 |
|||
} |
|||
option Steps { |
|||
type = IntegerEnum(1,16) |
|||
caption = "Steps" |
|||
details = "Number of inversion steps" |
|||
default = 4 |
|||
} |
|||
option Shift { |
|||
type = Boolean |
|||
caption = "Shift" |
|||
details = "Check to rotate initial chain by pi/N" |
|||
default = False |
|||
} |
|||
option RadiusMin { |
|||
type = Float |
|||
caption = "Radius Min" |
|||
details = "Minimum acceptable circle radius" |
|||
default = 0.001 |
|||
range = [0,) |
|||
} |
|||
#define ShowLevel(Index) |
|||
|
|||
divider { |
|||
caption = "Level #Index# Options" |
|||
} |
|||
option LR#Index# { |
|||
type = Boolean |
|||
caption = "Show Ring" |
|||
details = "Show ring of circles at level #Index#" |
|||
default = True |
|||
enabled = Steps >= #Index# |
|||
} |
|||
option LC#Index# { |
|||
type = Boolean |
|||
caption = "Show Center" |
|||
details = "Show center circle at level #Index#" |
|||
default = True |
|||
enabled = Steps >= #Index# |
|||
} |
|||
#end |
|||
|
|||
#include ShowLevel("1") |
|||
#include ShowLevel("2") |
|||
#include ShowLevel("3") |
|||
#include ShowLevel("4") |
|||
#include ShowLevel("5") |
|||
#include ShowLevel("6") |
|||
#include ShowLevel("7")]]></Instructions> |
|||
<PropertyValueOverrides> |
|||
<Option Name="Scale" Type="FloatOption" Value="2.22222222222222E+15" /> |
|||
<Option Name="AlternateAngle" Type="BooleanOption" Value="True" /> |
|||
<Option Name="LineWidth" Type="FloatOption" Value="0.00411522633744857" /> |
|||
<Option Name="ArgU" Type="FloatOption" Value="180" /> |
|||
<Option Name="ArgV" Type="FloatOption" Value="0" /> |
|||
<Option Name="Steps" Type="IntegerEnumOption" Value="1" /> |
|||
<Option Name="RadiusMin" Type="FloatOption" Value="1E-77" /> |
|||
<Option Name="LC1" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LC2" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LC3" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LC4" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LC5" Type="BooleanOption" Value="False" /> |
|||
<Option Name="LC6" Type="BooleanOption" Value="False" /> |
|||
</PropertyValueOverrides> |
|||
</OrbitTrap> |
|||
</OrbitTrapItem> |
|||
</OrbitTrapArray> |
|||
<OrbitTrapMasterController Id="c0ee11e5-31b4-4317-aa68-94f9da6964c6" Title="Pass Thru"> |
|||
<Instructions><![CDATA[ |
|||
comment: |
|||
|
|||
Return color computed by 1st controller. |
|||
|
|||
color: |
|||
|
|||
color = Controller.Color(0) |
|||
]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</OrbitTrapMasterController> |
|||
<OrbitTrapControllerArray> |
|||
<OrbitTrapController Id="e36679d9-f775-43b2-af28-3ac49a97c1ab" Title="Color Map - Dwell/Index" ContrastLuminance="True" ApplyDepth="False" Apply3D="False"> |
|||
<GradientArray /> |
|||
<TextureArray /> |
|||
<Instructions><![CDATA[ |
|||
comment: |
|||
|
|||
This controller colors each trap based on the |
|||
property 'Index Map' and the point's 'Trap Dwell' |
|||
'Trap Index' or 'Trap Delta'. You can define up to |
|||
16 colors and these are mapped to the index map |
|||
values. Offset can be used to shift the set of |
|||
colors with respect to value 0. |
|||
|
|||
If Cutouts are active, the trap is divided into |
|||
N sectors and a user defined percent of each |
|||
sector is inverted with respect to the 3D shading |
|||
effect. This gives the appearance that part of |
|||
the trap surface has been cutout or folded over. |
|||
|
|||
The Cutout effect only looks good if the trap |
|||
is a solid shape. For example, the 'Shape', |
|||
'Tangent Circles', 'Shapes' and 'Squares' |
|||
traps support a 'Solid' property that is used to |
|||
produce a solid figure. You should check this |
|||
property to display Cutouts. |
|||
|
|||
Also note that the Cutout effect only works if |
|||
the trap's angle is given relative to the center |
|||
of the solid shape. This is always the case when |
|||
the trap is composed of a single shape. However, |
|||
when the trap is composed of several shapes arranged |
|||
in a pattern like the 'Tangent Circles', 'Shapes' and |
|||
'Squares' traps, the angle is given relative to the |
|||
center of the pattern not the individual shapes. |
|||
In those cases, you will need to check the |
|||
'Alternate Angle' property on the properties page |
|||
for the specific trap so the angle is given relative |
|||
to the individual shapes. |
|||
|
|||
global: |
|||
|
|||
const Complex angleShift = SectorAngle / 360 |
|||
const Complex percentSolid = 1 - PercentCutout |
|||
|
|||
color: |
|||
|
|||
switch (IndexMap) { |
|||
case IndexMapTypes.TrapDwell: index = Sample.TrapDwellRaw |
|||
case IndexMapTypes.TrapIndex: index = Sample.TrapIndexRaw |
|||
case IndexMapTypes.TrapDelta: index = Sample.TrapDeltaRaw |
|||
case IndexMapTypes.Alternate1Index: index = Sample.Alternate1IndexRaw |
|||
} |
|||
color = Colors[WrapIndex(Offset + index, Count)] |
|||
|
|||
if (ApplyCutouts) { |
|||
r = Sectors * Wrap(Sample.TrapAngle - angleShift) |
|||
r = r - Int(r) |
|||
v = Abs(Sample.TrapValue) |
|||
|
|||
compositeHeight = IIf(r < percentSolid, v, Blend(0.75, 0.25, v)) |
|||
} else { |
|||
compositeHeight = Sample.TrapValue |
|||
} |
|||
|
|||
properties: |
|||
|
|||
divider { |
|||
caption = "Index Map" |
|||
} |
|||
enum IndexMapTypes { |
|||
TrapDwell, "Trap Dwell" |
|||
TrapIndex, "Trap Index" |
|||
TrapDelta, "Trap Delta" |
|||
Alternate1Index , "Alternate 1 Index" |
|||
} |
|||
option IndexMap { |
|||
type = IndexMapTypes |
|||
caption = "Index Map" |
|||
details = "Color index map" |
|||
default = IndexMapTypes.TrapDwell |
|||
} |
|||
divider { |
|||
caption = "Color Map" |
|||
} |
|||
option Count { |
|||
type = IntegerEnum(1,32) |
|||
caption = "Count" |
|||
details = "Number of colors to use" |
|||
default = 8 |
|||
} |
|||
option Colors { |
|||
type = ColorSet[Count] |
|||
caption = "Colors" |
|||
default = FF00AE, FF2020, FF8200, FFFF00, 00FF6C, 00FFFF, 4040FF, AE60FF |
|||
} |
|||
option Offset { |
|||
type = IntegerEnum(0,31) |
|||
caption = "Offset" |
|||
details = "Offset into set of colors" |
|||
default = 0 |
|||
} |
|||
divider { |
|||
caption = "Cutouts (Solid traps only)" |
|||
} |
|||
option ApplyCutouts { |
|||
type = Boolean |
|||
caption = "Active" |
|||
details = "Activate cutout effects" |
|||
default = False |
|||
} |
|||
option Sectors { |
|||
type = IntegerEnum(2,16) |
|||
caption = "Sectors" |
|||
details = "Number of sectors" |
|||
default = 2 |
|||
enabled = ApplyCutouts |
|||
} |
|||
option SectorAngle { |
|||
type = Float |
|||
caption = "Angle" |
|||
details = "Starting angle of 1st sector" |
|||
default = 0 |
|||
range = [-360,360] |
|||
enabled = ApplyCutouts |
|||
} |
|||
option PercentCutout { |
|||
type = Float |
|||
caption = "Percent Cutout" |
|||
details = "Percent of sector that is cutout" |
|||
range = [0,1] |
|||
default = 0.5 |
|||
enabled = ApplyCutouts |
|||
} |
|||
]]></Instructions> |
|||
<PropertyValueOverrides> |
|||
<Option Name="IndexMap" Type="EnumOption" Value="IndexMapTypes.TrapDelta" /> |
|||
<Option Name="Count" Type="IntegerEnumOption" Value="1" /> |
|||
<Option Name="Colors" Type="ColorSetOption" Value="00F47C" /> |
|||
</PropertyValueOverrides> |
|||
</OrbitTrapController> |
|||
</OrbitTrapControllerArray> |
|||
<SampleDataNormalizer> |
|||
<NormalizerDescriptor /> |
|||
</SampleDataNormalizer> |
|||
<SampleDataNormalizer> |
|||
<NormalizerDescriptor /> |
|||
</SampleDataNormalizer> |
|||
<SampleDataNormalizer> |
|||
<NormalizerDescriptor /> |
|||
</SampleDataNormalizer> |
|||
</OrbitTrapInfo> |
|||
<TransformationArray> |
|||
<Transformation Id="7fc4bc2c-b961-4431-b074-277d7b29842b" Title="Identity"> |
|||
<Instructions><![CDATA[]]></Instructions> |
|||
<PropertyValueOverrides /> |
|||
</Transformation> |
|||
</TransformationArray> |
|||
<TriangleMetricSet> |
|||
<Instructions><![CDATA[metric = p1]]></Instructions> |
|||
<TriangleMetric /> |
|||
<TriangleMetric /> |
|||
<TriangleMetric /> |
|||
</TriangleMetricSet> |
|||
</Fractal> |
BIN
∣❁∣✤✻ᕭᕮᗩߦറߦᗩᕭᕮ✻✤∣❁∣/◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇⠀ ⠀◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇/ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN⠀ ⠀ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN/ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄✣ⵙИN⩇ИNⵙ✣𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ/ꓨИꟼ.⅃MX.𐫰⊚ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ⊚𐫰.XML.PNG
BIN
∣❁∣✤✻ᕭᕮᗩߦറߦᗩᕭᕮ✻✤∣❁∣/◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇⠀ ⠀◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇◦୦◦◯◦୦◦◇⟠✣ᑐᑕ⟠🝍ꗳ🝍⟠ᑐᑕ✣⟠◇/ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN⠀ ⠀ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN◦୦◦◯◦୦◦ИN⟠ⵙИNⓄ◇Ⓞ🝊⟠🝊Ⓞ◇ⓄИNⵙ⟠ИN/ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄✣ⵙИN⩇ИNⵙ✣𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝊⩇Ⓞ🝍Ⱉ🝍Ⓞ⩇🝊𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄✣ᗱᗴᔓᔕᗱᗴ✣𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ/ꓨИꟼ.⅃MX.𐫰⊚ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᗱᗴ◇ᑐᑕ🝍ⵙᑐᑕⵙ🝍ᑐᑕ◇ᗱᗴ𖢄🝍Ⓞ✣ИN⟠ᑐᑕ⟠ИN✣Ⓞ🝍𖢄ᔓᔕⓄ🝍ᑐᑕ🝍Ⓞᔓᔕ⊚𐫰.XML.PNG
After Width: | Height: | Size: 276 KiB |
Loading…
Reference in new issue