Fractal generator: examples

Logo

 
The fractal generator is an application that the developers of Excel probably did not have in mind for their package. It creates graphical images of a certain type of fractals that can be constructed by linear transformations: rotations, line mirrors, multiplications and translations.

Screen dump

If you prefer to experiment with the fractal generator without having to start completely from scratch, you can use the following examples.


Fern (this is the example shown above)

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.7

0.15

0.15

0

Multiplying rotation / mirror operation

 

Origin: X:

0

0

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

3

-75

75

0

 

Multiplication:

0.8

0.3

0.3

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

3

2

2

0


Sierpinsky

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.33

0.33

0.33

0

Multiplying rotation / mirror operation

 

Origin: X:

0

0

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

0

0

0

0

 

Multiplication:

0.5

0.5

0.5

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

-0.5

0.5

0

 

Y:

0.5

-0.5

-0.5

0


Crystal

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.33

0.33

0.33

0

Multiplying rotation / mirror operation

 

Origin: X:

0

0

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

180

180

180

0

 

Multiplication:

0.5

0.5

0.5

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

-0.5

0.5

0

 

Y:

0.5

-0.5

-0.5

0


Lévy

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.5

0.5

0

0

Multiplying rotation / mirror operation

 

Origin: X:

0

0

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

45

-45

0

0

 

Multiplication:

0.7071

0.7071

0

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

-1

1

0

0

 

Y:

0

0

0

0


Curly

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.7

0.3

0

0

Multiplying rotation / mirror operation

 

Origin: X:

0

1

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

-45

0

0

0

 

Multiplication:

0.8

0.5

0

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

0

0

0

0


Pointy

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.6

0.2

0.2

0

Multiplying rotation / mirror operation

 

Origin: X:

0

0

0

0

 

Y:

0

-1

-1

0

 

Angle (degrees):

0

45

-45

0

 

Multiplication:

0.5

0.5

0.5

0

 

Rotate (R) / mirror (M):

R

M

M

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

0

0

0

0


Spirals

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.92

0.08

0

0

Multiplying rotation / mirror operation

 

Origin: X:

0

1

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

22.5

0

0

0

 

Multiplication:

0.95

0.2

0

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

0

0

0

0


Squares

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.25

0.25

0.25

0.25

Multiplying rotation / mirror operation

 

Origin: X:

1

-1

-1

1

 

Y:

1

-1

1

-1

 

Angle (degrees):

0

0

0

0

 

Multiplication:

0.4

0.4

0.4

0.4

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

0

0

0

0


Lake shore

 

Operation 1

Operation 2

Operation 3

Operation 4

 

Probability:

0.5

0.5

0

0

Multiplying rotation / mirror operation

 

Origin: X:

0

1

0

0

 

Y:

0

0

0

0

 

Angle (degrees):

90

0

0

0

 

Multiplication:

0.7071

0.7071

0

0

 

Rotate (R) / mirror (M):

R

R

R

R

Translation

 

Distance: X:

0

0

0

0

 

Y:

0

0

0

0


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