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fracZi

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fracZi render details
Z' = (z^(2.3/(c*@com (1,1.8))))
A = 0.0
B = 0.0
X1= -0.32695178755144033
Y1= -0.5824464120370364
X2= -0.12714193672839502
Y2= -0.22722889946273367
ITS=1.0
INF=4.0
C = ((n / 2 ) / p) / p *@log(@abs(b)) / ( 2 ^ m)
Y = @log(@abs(a)) / ( 2 ^ m)
M = 1 - ((n / 2 ) / p) *@log(@abs(a)) / ( 2 ^ m)
K = @log(@abs(b)) / ( 2 ^ m)

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fracZi

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fracZi render details
Z' = b^@abs (a)+c
A = 0.0
B = 0.0
X1= 1.7586666666666657
Y1= -2.0702222222222204
X2= 2.6079999999999997
Y2= -0.5602962962962934
ITS=50.0
INF=5000.0
C = (n ) / p
Y = @abs(z)/m
M = 1 - ((n ) / p)
K = 0

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fracZi

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fracZi render details
Z' = z ^(a-b )+c
A = 0.0
B = 0.0
X1= -0.06666666666666665
Y1= -1.0503703703703702
X2= 0.9999999999999998
Y2= 0.8459259259259255
ITS=23.0
INF=34.0
C = (n ) / p
Y = @log(@abs(a)) / ( 2 ^ n)
M = 1 - ((n ) / p)
K = @log(@abs(b)) / ( 2 ^ n)

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fracZi

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fracZi render details
Z' = z * z +c
A = 0.0
B = 0.0
X1= -4.0
Y1= -6.5
X2= 4.0
Y2= 7.722222222222221
ITS=2.0
INF=50.0
C = (n / 2 ) / p
Y = @log(@abs(a)) / ( 2 ^ n)
M = 1 - ((n / 2 ) / p)
K = @log(@abs(b)) / ( 2 ^ n)

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fracZi

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fracZi render details
Z' = z ^ z /c
A = 0.0
B = 0.0
X1= 0.01145182376170284
Y1= -0.9612822155457843
X2= 1.0292424946655674
Y2= 0.8481234216166416
ITS=4.0
INF=4.0
C = (n / 2 ) / p
Y = @log(@abs(a)) / ( 2 ^ n)
M = 1 - ((n / 2 ) / p)
K = @log(@abs(a)) / ( 2 ^ n)

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fracZi

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fracZi render details
Z' = b^@abs (a)+c
A = 0.0
B = 0.0
X1= 2.0087481481481473
Y1= -1.203194444444442
X2= 2.2953981481481476
Y2= -0.6935944444444415
ITS=150.0
INF=6666.6665
C = (n ) / p
Y = @abs(z)/m
M = 1 - ((n ) / p)
K = 0

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fracZi

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fracZi render details
Z' = c^@abs (a-b)
A = 0.0
B = 0.0
X1= -8.146666666666668
Y1= -15.064444444444444
X2= 7.533333333333334
Y2= 12.811111111111117
ITS=4.0
INF=5.0E7
C = (n ) / p
Y = @log(@abs(a)) / ( 2 ^ n)
M = 1 - ((n ) / p)
K = @log(@abs(b)) / ( 2 ^ n)

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fracZi

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fracZi render details
Z' = z ^b +(c^a)
A = 0.0
B = 0.0
X1= -0.6654503172153633
Y1= 0.6605452674897115
X2= -0.4146787122770915
Y2= 1.106361454046639
ITS=7.0
INF=1000.0
C = (n / 2 ) / p
Y = @log(@abs(a)) / ( 2 ^ n)
M = 1 - ((n / 2 ) / p)
K = @log(@abs(b)) / ( 2 ^ n)

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fracZi

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fracZi render details
Z' = z * z +c
A = 0.0
B = 0.0
X1= -2.1333333333333333
Y1= -2.8777777777777778
X2= 1.0777777777777775
Y2= 2.8308641975308633
ITS=2.0
INF=7.9999998
H = @log(@abs(n)) / ( 2 ^ n)
S = 1
L = 1 - ((n / 2 ) / p)

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fracZi

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fracZi render details
Z' = (z^a + c^a)
A = 0.0
B = 0.0
X1= 1.2756853411862907
Y1= -0.9958988984549697
X2= -1.269219702863584
Y2= -0.9844044303257135
ITS=254.0
INF=368.0
C = @sin (a +b)
Y = ((n / 2 ) / p) *@log(@abs(b*a)) / ( 2 ^ m)
M = 1(n/p)/2
K = ( ( a*8)/23)+b

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Nirdh Mehta's profile photo
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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