1. © 2009 Rick Diefenderfer Creating Christian Communities™ ™

2. 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

3. 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

4. What shape is a flower? What are its characteristics? “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

5. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

6. “When I look at plants, what I find beautiful is their shape and form. But there is also another layer of beauty. It is a hidden beauty… Not what we see… It is a beauty of an understanding of the mechanisms which bring this form about.” Dr. “Przemyslaw Prusinkiewicz” “When I look at plants, what I find beautiful is their shape and form. But there is also another layer of beauty. It is a hidden beauty… Not what we see… It is a beauty of an understanding of the mechanisms which bring this form about.” Dr. “Przemyslaw Prusinkiewicz” “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

7. 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’. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

8. 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)

9. Wikipedia (The Free Encyclopedia) Mathematician Benoit Mandelbrot pointed out that these old forms have 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 forms have several striking characteristics. They possess aesthetic appeal, appear to be a complicated structure yet, arise from a simple definition.

10. 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 (The Free Encyclopedia)

11. Very intricate shapes can be created by following very SIMPLE RULES. SIERPINSKI GASKET Wikipedia (The Free Encyclopedia)

12. 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. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

13. 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 (The Free Encyclopedia)

14. 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

15. 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’. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

16. ‘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. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

17. 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 Free Encyclopedia)

18. The ‘L-system’ describes the mechanism that plants follow to accomplish growth. The ‘L-system’ describes the mechanism that plants follow to accomplish growth. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

19. 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 Free Encyclopedia)

20. The ‘L-system’ is simply a set of repeatable rules that can be used to create self-similar structures. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

21. An ‘L-system’ might state that the top of a branch will always form 2 new branches and 3 new tops. The ‘L-system’ is simply a set of repeatable rules that can be used to create self-similar structures. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

22. 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 structure is formed. The ‘L-system’ is simply a set of repeatable rules that can be used to create self-similar structures. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

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

24. 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

25. 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.” “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

26. 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.” “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

27. 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. “Life by Numbers; Patterns of Nature” Tape 3 of 7; Produced by WQED, Pittsburgh © 1998

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

29. Shouldn’t the principles of ‘fractal-geometry’ --self-similarity and ‘L-systems’-- be followed when ‘planting’ a simple cell-based church? Shouldn’t the principles of ‘fractal-geometry’ --self-similarity and ‘L-systems’-- be followed when ‘planting’ a simple cell-based church? Rick Diefenderfer Creating Christian Communities ™ © 2009

30. “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]

31. ‘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. Rick Diefenderfer Creating Christian Communities ™ © 2003

32. 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. Rick Diefenderfer Creating Christian Communities ™ © 2009

33. 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

34. 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.” Rick Diefenderfer Creating Christian Communities ™ © 2009

35. 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 ™ Rick Diefenderfer Creating Christian Communities ™ © 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.”

36. permits us to Live simply that others may simply live. permits us to Live simply that others may simply live. Rick Diefenderfer Creating Christian Communities ™ © 2009 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

37. Please visit CreatingChristianCommunities.com for more information Rick Diefenderfer Creating Christian Communities ™ © 2009