Lesson 1

• What is a regularity in the context of patterns in nature?


  A regularity is the fact that the same thing always happens in the same circumstances.
• How is a pattern defined?

  A pattern is a discernible regularity in the world or in a man-made design.
• What are patterns in nature?

  Patterns in nature are visible patterns found in the natural world.
• What does symmetry mean in the context of patterns?

  Symmetry means agreement in dimensions, due proportion, and arrangement.
• What is a spiral?


  A spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
• What is a meander?


  A meander is one of a series of regular sinuous curves, bends, loops, turns, or windings in the channel of a river, stream, or other watercourse.
• What is a wave?

  A wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.
• What is foam?

  Foam is a substance formed by trapping pockets of gas in a liquid or solid.
• What is a tessellation?

  A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
• What is a fracture?


  A fracture or crack is the separation of an object or material into two or more pieces under the action of stress.
• What are stripes?


  Stripes are made by a series of bands or strips, often of the same width and color along the length.
• What is a fractal?

  A fractal is a never-ending pattern that is infinitely complex and self-similar across different scales.
• How are fractals created?

  Fractals are created by repeating a simple process over and over in an ongoing feedback loop.
• What are affine transformations?


  Affine transformations are the processes of rotation, reflection, and scaling.
• What is the Fibonacci sequence?

  The Fibonacci sequence is characterized by the fact that every number after the first two is the sum of the two preceding ones.
• What are the first few numbers in the Fibonacci sequence?

  The first few numbers in the Fibonacci sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
• What is the significance of the Fibonacci sequence in nature?

  It is often associated with the ideal expansion pairs of rabbits over the course of one year.
• What patterns can be observed in the Fibonacci sequence regarding even and multiple terms?

  Every 3rd term is even, every fourth term is a multiple of three, and every fifth term is a multiple of five.
• What is the formula for the Fibonacci sequence?

  The formula is $A_n =$$A_{n-1} +$$A_{n-2}$, where $A_n$ is the nth term in the sequence.
• What do $A_{n-1}$ and $A_{n-2}$ represent in the Fibonacci formula?


  $A_{n-1}$ is the previous term in the sequence and $A_{n-2}$ is the second previous term in the sequence.