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09_MandelBrot_Formulas

MandelBrot_Formulas

MandelBrot_Formulas

MandelBrot_Formulas

script_type

Description

Formula_Category

z^next=z^2+c

MandelBrot_Formula

Classic Mandelbrot set

classic

z^next=z^3+c

MandelBrot_Formula

Cubic Multibrot

multibrot

z^next=z^4+c

MandelBrot_Formula

Quartic Multibrot

multibrot

z^next=z^2+(0.285+0.01i)

MandelBrot_Formula

Julia set with specific c value

julia

z^next=z^3+(0.285+0.01i)

MandelBrot_Formula

Cubic Julia variant

julia

z^next=z^4+(0.285+0.01i)

MandelBrot_Formula

Quartic Julia variant

julia

z₀=c;z^next=z^2+c

MandelBrot_Formula

Burning Ship fractal style seed

modified_seed

z₀=1;z^next=z^2+c

MandelBrot_Formula

Alternative seed value

modified_seed

z^next=z^2+c+ε·sin(z)

MandelBrot_Formula

Sinusoidal perturbation

perturbation

z^next=z^2+c+ε·z̄

MandelBrot_Formula

Conjugate perturbation

perturbation

z^next=z^2·c

MandelBrot_Formula

Multiplicative instead of additive

operation_change

z^next=z^2/(1+c·z)

MandelBrot_Formula

Rational function

operation_change

z^next=|z|^2+c

MandelBrot_Formula

Using absolute value

operation_change

z^next=z^2+c̄

MandelBrot_Formula

Using complex conjugate of c

hybrid

z^next=z·z̄+c

MandelBrot_Formula

Using complex modulus squared

hybrid

z^next=Re(z)^2-Im(z)^2+2·Re(z)·Im(z)i+c

MandelBrot_Formula

Expanded complex square

hybrid

z^next=z^2+c;w^next=w^2+d

MandelBrot_Formula

4D extension with two complex variables

higher_dimension

z^next=z^2+w;w^next=w^2+c

MandelBrot_Formula

Coupled iteration

higher_dimension

z^next=z^2+c·e^(i·t)

MandelBrot_Formula

Rotating c over time parameter t

time_varying

z^next=z^(2+0.1·sin(t))+c

MandelBrot_Formula

Oscillating exponent

time_varying

q^next=q^2+c

MandelBrot_Formula

Using quaternions

quaternion

q^next=q·a·q^(-1)+c

MandelBrot_Formula

Quaternion rotation and translation

quaternion

z^next=z^x+c

MandelBrot_Formula

Generalized form with variable exponent

generalized

z^next=z̄^2+c

MandelBrot_Formula

Tricorn/Mandelbar set

tricorn

r=2;zr=abs(z)>r?r/abs(z):1;z^next=zr·z+c

MandelBrot_Formula

Mandelbox fractal

mandelbox

z^next=(|Re(z)|+|Im(z)|·i)^2+c

MandelBrot_Formula

Burning Ship fractal

burning_ship

z^next=z-(z^3-1)/(3·z^2)+c

MandelBrot_Formula

Nova fractal (based on Newton's method)

nova

z₀=c;z₁=0;z^next=z^2+c+d·z_{n-2}

MandelBrot_Formula

Phoenix fractal with prior history

phoenix

z^next=((z^2+c-1)/(2·z+c-2))^2

MandelBrot_Formula

Magnet fractal type I

magnet

r^n·(sin(θ·n)cos(φ·n)

MandelBrot_Formula

sin(θ·n)sin(φ·n)

mandelbulb

z^next=f(z)+c

MandelBrot_Formula

Template for general complex function iteration

general_complex_analysis

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