© 2009 Rick Diefenderfer Creating Christian Communities™ ™

© 2009

Rick DiefenderferCreating Christian Communities™

™

May a shift in thinking occur within the cell-church movement with an understanding

of the ‘fractal’ characteristics of ‘self-similarity’.

Rick Diefenderfer

May a shift in thinking occur within the cell-church movement with an understanding

of the ‘fractal’ characteristics of ‘self-similarity’.

Rick Diefenderfer

One of the greatest powers of mathematics is its

power to describe things:

One of the greatest powers of mathematics is its

power to describe things:

CIRCLES

TRIANGLES

RECTANGLES

These geometrical shapes can be used to describe man-made

things with remarkable precision.

These geometrical shapes can be used to describe man-made

things with remarkable precision.

“Life by Numbers; Patterns of Nature”Tape 3 of 7; Produced by WQED, Pittsburgh

© 1998

What shape is a flower?What shape is a flower?

What are its characteristics?What are its characteristics?


© 1998


© 1998

“When I look at plants, what I findbeautiful is their shape and form.But there is also another layer ofbeauty. It is a hidden beauty…

Not what we see… It is a beauty ofan understanding of the mechanisms

which bring this form about.”

Dr. “Przemyslaw Prusinkiewicz”

“When I look at plants, what I findbeautiful is their shape and form.But there is also another layer ofbeauty. It is a hidden beauty…

Not what we see… It is a beauty ofan understanding of the mechanisms

which bring this form about.”

Dr. “Przemyslaw Prusinkiewicz”


© 1998

Dr. Prusinkiewicz studies plant growth. And, in his work, he turns to a ‘new geometry’

that describes nature’s forms -- ‘fractals’.

Dr. Prusinkiewicz studies plant growth. And, in his work, he turns to a ‘new geometry’

that describes nature’s forms -- ‘fractals’.


© 1998

A fractal is a geometric shape that can be split into parts, each of which is a reduced-size copy of the whole.

A fractal is a geometric shape that can be split into parts, each of which is a reduced-size copy of the whole.

Wikipedia

(The Free Encyclopedia)

Wikipedia


Mathematician Benoit Mandelbrot pointed out that these old formshave several striking characteristics. They possess aesthetic appeal,

appear to be a complicated structure yet, arise from a simple definition.

Mathematician Benoit Mandelbrot pointed out that these old formshave several striking characteristics. They possess aesthetic appeal,

appear to be a complicated structure yet, arise from a simple definition.

To create a classical fractal(known as the ‘Koch Snowflake’)…

• take a triangle…

• add a triangle to each side…

• and repeat the rule forever.

Wikipedia


Very intricate shapes can be

created by following very

SIMPLE RULES.

SIERPINSKI GASKET

Wikipedia


Nature is full of fractals. Consider the ‘tree’. The small branches look similar to the bigger branches which look similar to the entire tree.

Nature is full of fractals. Consider the ‘tree’. The small branches look similar to the bigger branches which look similar to the entire tree.


© 1998

The fractal characteristic where small parts

look like big parts is called ‘self-similarity’.

The fractal characteristic where small parts

look like big parts is called ‘self-similarity’.

Wikipedia


Dr. Prusinkiewicz says, “There was a period in my life when the idea of

‘self-similarity’ was so widely present, particularly in plants, that I was looking for it almost

everywhere.”

Dr. Prusinkiewicz says, “There was a period in my life when the idea of

‘self-similarity’ was so widely present, particularly in plants, that I was looking for it almost

everywhere.”“Life by Numbers; Patterns of Nature”

Tape 3 of 7; Produced by WQED, Pittsburgh© 1998

To Dr. Prusinkiewicz, it seems like nature relies on fractal geometry and to capture the fractal nature of plants,

he turns to a mathematical tool called the ‘L-system’.

To Dr. Prusinkiewicz, it seems like nature relies on fractal geometry and to capture the fractal nature of plants,

he turns to a mathematical tool called the ‘L-system’.


© 1998

‘L-systems’ describe the growth process of living organisms such as the branching patterns of plants.‘L-systems’ describe the growth process of living

organisms such as the branching patterns of plants.


© 1998

Have you noticed how the branches of plants branch out in very regular patterns?

A main branch might branch into two, then each into another two, again, each new one into another two, etc.

Look at the arrangement of the leaves and you'll notice they consist of an organized pattern.

(Go out into the garden and check this out)

It is as if someone decided on some precise instructions

of how plants are to grow !

Have you noticed how the branches of plants branch out in very regular patterns?

A main branch might branch into two, then each into another two, again, each new one into another two, etc.

Look at the arrangement of the leaves and you'll notice they consist of an organized pattern.

(Go out into the garden and check this out)

It is as if someone decided on some precise instructions

of how plants are to grow !

Wikipedia


The ‘L-system’ describes the mechanism

that plants follow to accomplish growth.

The ‘L-system’ describes the mechanism

that plants follow to accomplish growth.


© 1998

An ‘L-system’ is simply a process of a repetitive system to generate self-similar fractal structures.An ‘L-system’ is simply a process of a repetitive

system to generate self-similar fractal structures.

Wikipedia


The ‘L-system’ is simply a set ofrepeatable rules that can be usedto create self-similar structures.


© 1998

An ‘L-system’ might state that the top of a branch will always form 2 new branches and 3 new tops.



© 1998

An ‘L-system’ might state that the top of a branch will always form 2 new branches and 3 new tops.

If we repeat this simple process,a complex branching structureis formed.



© 1998

To model a lilac on a computer, Dr. Prusinkiewicz first creates a simple ‘L-system’. Next, he takes careful measurements of the branching structures. With this information, he refines the ‘L-

system’ to closer reflect reality.

To model a lilac on a computer, Dr. Prusinkiewicz first creates a simple ‘L-system’. Next, he takes careful measurements of the branching structures. With this information, he refines the ‘L-

system’ to closer reflect reality.“Life by Numbers; Patterns of Nature”


Once the branching structure is complete, he then adds the final touch by creating

‘self-similar’ flower blossoms.

Once the branching structure is complete, he then adds the final touch by creating

‘self-similar’ flower blossoms.“Life by Numbers; Patterns of Nature”Tape 3 of 7; Produced by WQED, Pittsburgh

© 1998

Dr. Prusinkiewicz says, “It is very exciting to see a structure we used to think of as very complex turns out to be very simple in principle.

The plant is repeating the same thing over and over again. But since it is doing it in so many places, the plant winds up with a structure which looks very complex to us but, in essence, it is just intricate.”

Dr. Prusinkiewicz says, “It is very exciting to see a structure we used to think of as very complex turns out to be very simple in principle.

The plant is repeating the same thing over and over again. But since it is doing it in so many places, the plant winds up with a structure which looks very complex to us but, in essence, it is just intricate.”


© 1998

Today, mathematical equations are producing a striking new view of the natural world. This new view suggests a rather provocative idea—

“Much of the complexity we see in the natural world may be the result of some very simple principles.”

Today, mathematical equations are producing a striking new view of the natural world. This new view suggests a rather provocative idea—

“Much of the complexity we see in the natural world may be the result of some very simple principles.”


© 1998

New geometry of fractals, self-similarity and ‘L-systems’

is present everywhere in nature’s plant forms.

New geometry of fractals, self-similarity and ‘L-systems’

is present everywhere in nature’s plant forms.


© 1998

Dr. Prusinkiewicz says, “Mathematics is not playing with numbers and doing accounting.

Mathematics is dealing with ideas in a creative yet very precise way.”

Dr. Prusinkiewicz says, “Mathematics is not playing with numbers and doing accounting.

Mathematics is dealing with ideas in a creative yet very precise way.”“Life by Numbers; Patterns of Nature”


Shouldn’t the principles of ‘fractal-geometry’ --self-similarity and ‘L-systems’-- be followedwhen ‘planting’ a simple cell-based church?

Shouldn’t the principles of ‘fractal-geometry’ --self-similarity and ‘L-systems’-- be followedwhen ‘planting’ a simple cell-based church?

Rick DiefenderferCreating Christian Communities ™

© 2009

“It is imperative that we have a clear picture of what we want to be in our mature and final state.

We can't just hope that we end up that way; we must start out that way!

To do so, we must have a mature template to follow throughout the entire process.

A highly developed model can be reproduced endless number of times

until the city is saturated with cell groups that are part of a predictable system where [Jesus Christ is ALL and in ALL]

and the Holy Spirit can move freely.” Billy Hornsby

“Picture of a Pure Cell Church”Bethany Cell Conference Manual

Feb. 1997; p.5-7

[Emphasis Added as requested by Dr. Ralph Neighbour]

“It is imperative that we have a clear picture of what we want to be in our mature and final state.

We can't just hope that we end up that way; we must start out that way!

To do so, we must have a mature template to follow throughout the entire process.

A highly developed model can be reproduced endless number of times

until the city is saturated with cell groups that are part of a predictable system where [Jesus Christ is ALL and in ALL]

and the Holy Spirit can move freely.” Billy Hornsby

“Picture of a Pure Cell Church”Bethany Cell Conference Manual

Feb. 1997; p.5-7

[Emphasis Added as requested by Dr. Ralph Neighbour]

‘Fractal geometry’ is a key to understanding that

what appears to be a complicated cell-church

model

actually stems from a very simple definition.‘Fractal geometry’ is a key to understanding that

what appears to be a complicated cell-church

model

actually stems from a very simple definition.


© 2003

While it is true that ‘all living things grow with time’,

the fact that they do does not prove Darwin’s theory of evolution to be correct.


© 2009

In his book, “Creating Christian Communities – The Structure & Strategy of a Simple Cell-Based Church System”, Rick Diefenderfer writes,

• There is an old German maxim that asks, "Why be so simple when complexity is so beautiful?”

• Gandhi is quoted to have said, "Live simply that others may simply live”.

• Larry Stockstill, pastor of Bethany World Prayer Center, Baker, Louisiana, writes, "True genius is not the ability to make things complex, but the ability to make them simple… We must simplify”.Rick Diefenderfer

Creating Christian Communities ™ © 2009

A. Because ‘fractal geometry’ reveals much of the complexity we see in the natural world is merely the result of some very simple principles.

Q. "Why be so simple when complexity is

so beautiful?”

“True genius is not the ability

to make things complex,

but the ability to make

them simple.”


© 2009

A snapshot of ‘fractal geometry’ applied to the Structure and Strategy of a Simple Cell-Based Church System™

A snapshot of ‘fractal geometry’ applied to the Structure and Strategy of a Simple Cell-Based Church System™


© 2009

“The simple cell-based church system exists to fulfill a balanced fourfold purpose by gathering every Sunday for the twofold purpose of worship and receiving biblical instruction and scattering as cells, meeting in homes throughout the city, for the twofold purpose of fellowship and expressions of our

faith in Jesus Christ.”

“The simple cell-based church system exists to fulfill a balanced fourfold purpose by gathering every Sunday for the twofold purpose of worship and receiving biblical instruction and scattering as cells, meeting in homes throughout the city, for the twofold purpose of fellowship and expressions of our

faith in Jesus Christ.”

permits us to

Live simply that others may simply live.

permits us to

Live simply that others may simply live.


© 2009

Much of the complexity we see in the natural world may be the result

of some very simple principles.

Much of the complexity we see in the natural world may be the result

of some very simple principles.

The Structure & Strategy of a Simple Cell-Based Church System

The Structure & Strategy of a Simple Cell-Based Church System

Please visit CreatingChristianCommunities.co

m for more information

Please visit CreatingChristianCommunities.co

m for more information


© 2009

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© 2009 Rick Diefenderfer Creating Christian Communities™ ™