### fracZi

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Z' = @com(1,a)*z * @tan(b) + c

~~-----Seeds~~

~~A = 0.0, B = 0.0~~

~~-------Domain~~

~~X1=-4.0, Y1=-6.5~~

~~to~~

~~X2=4.0, Y2=7.722222222222221~~

~~-------Bailout Parameters~~

~~Max Iterations= 2.0~~

~~Infinity= 50.0~~

~~-------Color Representation~~

~~Hue = 1(a/b)~~

~~Saturation = b~~

~~Level = 1~~@abs (a/b)

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rendered with fracZi for Android

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Z' = z * @tan(z) + c

~~-----Seeds~~

~~A = 0.0, B = 0.0~~

~~-------Domain~~

~~X1=-1.5626157407407406, Y1=-0.8563194444444449~~

~~to~~

~~X2=-0.6059490740740741, Y2=0.8444212962962956~~

~~-------Bailout Parameters~~

~~Max Iterations= 80.0~~

~~Infinity= 300.0~~

~~-------Color Representation~~

~~Hue = 1(a/b)~~

~~Saturation = 1~~

~~Level = 1~~@abs (a/b)

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rendered with fracZi for Android

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Z' = @sin(@com (b,1))*@sin (@com(1, a))+c

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-0.17197627314814823, Y1=-1.886838991769548

to

X2=-0.030355902777777853, Y2=-1.6350694444444451

-------Bailout Parameters

Max Iterations= 13.0

Infinity= 9.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-0.17197627314814823, Y1=-1.886838991769548

to

X2=-0.030355902777777853, Y2=-1.6350694444444451

-------Bailout Parameters

Max Iterations= 13.0

Infinity= 9.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

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Z' = @sin(@com (b,1))*@sin (@com(1, a))+@exp (c)

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 2.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 2.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

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Z' = c/(z ^ @sin(z))

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-0.18454003333333335, Y1=0.5588454828703703

to

X2=-0.16691164328703706, Y2=0.5901848429526748

-------Bailout Parameters

Max Iterations= 10.0

Infinity= 4900.0

-------Color Representation

Red = N / P

Green = A / B

Blue = B / A

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-0.18454003333333335, Y1=0.5588454828703703

to

X2=-0.16691164328703706, Y2=0.5901848429526748

-------Bailout Parameters

Max Iterations= 10.0

Infinity= 4900.0

-------Color Representation

Red = N / P

Green = A / B

Blue = B / A

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Z' = z * z + C

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3430826663274364, Y1=0.054984013626995905

to

X2=0.344570528551409, Y2=0.05762910202516946

-------Bailout Parameters

Max Iterations= 18.0

Infinity= 40.0

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3430826663274364, Y1=0.054984013626995905

to

X2=0.344570528551409, Y2=0.05762910202516946

-------Bailout Parameters

Max Iterations= 18.0

Infinity= 40.0

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

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In their circles

5 people

Z' = z * @tan(z) + c

~~-----Seeds~~

~~A = 0.0, B = 0.0~~

~~-------Domain~~

~~X1=-2.9333333333333336, Y1=-6.088888888888889~~

~~to~~

~~X2=-0.6333333333333333, Y2=-1.9999999999999991~~

~~-------Bailout Parameters~~

~~Max Iterations= 41.0~~

~~Infinity= 30.0~~

~~-------Color Representation~~

~~Hue = 1(a/b)~~

~~Saturation = b~~

~~Level = 1~~@abs (a/b)

rendered with fracZi for Android

rendered with fracZi for Android

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Z' = z * @tan(z) + c

~~------Seeds~~

~~A = 0.0, B = 0.0~~

~~-------Domain~~

~~X1=-0.7001064814814812, Y1=-0.47452623456790155~~

~~to~~

~~X2=-0.5896867283950615, Y2=-0.27822445130315543~~

~~-------Bailout Parameters~~

~~Max Iterations= 40.0~~

~~Infinity= 500.0~~

~~-------Color Representation~~

~~Cyan = 1~~

~~Yellow = @abs(a/b)~~

~~Magenta = @log(@abs(z)) / ( 2 ^ n)~~

~~blacK = 1~~@log(z)

rendered with fracZi for Android

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Z' = @sin(@com (b,1))*@sin (@com(1, a))+@exp (c)

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 4.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 4.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

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Z' = @sin(@com (b,1))*@sin (@com(1, a))+@exp (c)

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 1.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=-4.0, Y1=-6.5

to

X2=4.0, Y2=7.722222222222221

-------Bailout Parameters

Max Iterations= 1.0

Infinity= 1.0

-------Color Representation

Red = b/m

Green = @log(@abs(a)) / ( 2 ^ n) -((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)

Blue = @log(@abs(b)) / ( 2 ^ m)

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Working on a color remap function

Z' = z * z + C

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3439810502646191, Y1=0.05669561015239784

to

X2=0.343981185812143, Y2=0.05669585112577361

-------Bailout Parameters

Max Iterations= 52.0

Infinity= 52.0

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

rendered with fracZi for Android

Z' = z * z + C

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3439810502646191, Y1=0.05669561015239784

to

X2=0.343981185812143, Y2=0.05669585112577361

-------Bailout Parameters

Max Iterations= 52.0

Infinity= 52.0

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

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Z' = z * z + C

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3352346018493389, Y1=0.04780630465640257

to

X2=0.34700669856648514, Y2=0.06873447659799589

-------Bailout Parameters

Max Iterations= 124.0

Infinity= 6.760000000000001

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

rendered with fracZi for Android

-------Seeds

A = 0.0, B = 0.0

-------Domain

X1=0.3352346018493389, Y1=0.04780630465640257

to

X2=0.34700669856648514, Y2=0.06873447659799589

-------Bailout Parameters

Max Iterations= 124.0

Infinity= 6.760000000000001

-------Color Representation

Red = @bound (b/m,0,1)

Green = @bound (a/m,0,1)

Blue = .5

rendered with fracZi for Android

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People

In their circles

5 people

Contact Information

Contact info

- jack@jacknorth.com
| |

Story

Tagline

FracZi is a true color fractal rendering app that allows you to enter formulas for the main equationand rendering color in three color modes.

Introduction

Using fracZi

When fracZi starts, it begins calculating the default fractal. The fractal is displayed in stages on your screen. At each stage, the number of iterations and effective infinity is increased. FracZi displays the rendering progress at the top of your screen.

At any time, you can choose to zoom or pan your view of the fractal. To zoom or pan, draw a diagonal line with ONE of your fingers on the screen (fracZi will highlight the area for you). Once you lift your finger, fracZi will ask if you want to Zoom or Center. If you select zoom, fracZi will begin calculating the fractal so that the area you selected fills the screen. If you select 'Center,' fracZi will begin calculating the fractal so that the area you selected is centered in the screen.

When you choose to zoom or center, fracZi displays a preview on your screen and immediately begins recalculating the fractal based on the new location. The preview image may appear pixilated until fracZi recalculates the pixels.

fracZi comes with several fractals to explore. To change the fractal you're exploring, use your device's menu button, and then select 'Open.' Choose a fractal from those displayed.

Any fractals you have saved will be available to load in addition to the fractals provided with fracZi. Once your fractal is loaded, you can open the 'Custom' screen where can access the formulas and rendering details.

fracZi allows you to control many aspects of the rendering process. You can enter formulas for the main equation, seeds, infinity, iterations, red, green, blue, hue, saturation, balance (brightness), cyan, magenta, yellow, and black. Images can be shared and/or saved as a PNG file.

Formulas are constructed of tokens and tokens can either be an operator (=,-,*,/,^) or an operand. Operands can be literal numbers, variables, functions, or even sub-formula.

Supported variable are:

Z (The complex number that is fed back into the equation. Z= A + Bi)

A (the real part of Z)

B (the imaginary part of Z)

C (the current position in the x, y coordinate system C= X + Yi)

X (the real part of C)

Y (the imaginary part of C)

N (Number of iterations before breaking out of the loop)

P (the total number of iteration allowed before breaking out of the loop)

T (the maximum iterations before rendering stops)

M (the current infinity)

I (the current infinity)

Formulas also support functions. The allowed functions are

LOG

EXP

SIN

COS

TAN

COM

ABS

MAX

MIN

BOUND

WRAP

This formula

Z ^ 2 * C

produces the famous Mandelbrot set.

If we used this formula for red

Red = N / P

We would see the Mandelbrot set because when N = P, the maximum iterations were reached. In this case, N/P = 1, the maximum amount of red is produced. In areas where infinity was reached quickly (2 iterations out of 100, the amount of red would be lower because N / P = 2 /10 = .2

fracZi supports three color modes; RGB (red, green, blue), HSB (Hue, Saturation, and Brightness), and CYMK (Cyan, Yellow, Magenta, and Black).

Regardless of the mode you select, each attribute in the mode accepts a decimal value between 0 and 1. 0 is none and 1 is full. For instance,

Red = N / P

Green = A / M

Blue = B / M

Or,

HUE = .33334

SAT = @ABS(M/A)

LEVEL = @BOUND(B / M,.5,1)

The final color will be a mix of red, green, and blue (or HSB) in the ratios returned from the equations.

The same concept applies to HSB. For hue, 0 = 0 degrees, and 1 = 360 degrees. For saturation, 0 is no saturation and 1 is full saturation, etc

Links

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