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Other :: Comparing patterns & Self similarity :: In Arts & Nature :: Visual comparison using Dot Plots

Self similarity appears to be one of nature’s most favored design principles. Self-similarity is so widespread and important in nature, the arts and society. It is generating complexity from a simple initial pattern and a set of transformations on that pattern.
Dot plot is a simple graphical approach for the visual comparison of two sequences or find self similarity. To compare place one sequence on the vertical axis of a 2D grid (or matrix) and the other on the horizontal. In its simplest form, a dot is placed where the horizontal and vertical sequence values match.
Lets see how we can compare two sequences using dot matrix method. Let us take the first sequence AGCTAGGA and the second sequence GACTAGGC.
Picture

Picture

Long sequences can also be compared using smaller plots. By plotting a sequence against itself it is possible to find internal repeats, reveal tandem genes, repeated domains in proteins, or regions of low complexity where the same character is repeated.
Dot Plots have a long history :
  • Gibbs and Mclntyre 1970
  • Maizel and Lenk 1981
Self-Similarity in Fractal Geometry
Picture
Start with a filled in triangle connect the midpoints of each side and remove middle triangle. Repeat this process the resulting shape will be a self similar Sierpinski triangle which exhibits self similar behavior. The idea being that if we were to look at just a portion, that piece if we were to zoom in is identical to the whole. Are you intrigued? Learn more about patterns in Nature here..


Picture

keentween

  • Ask
  • FAQ
  • Summer 2020 Tutoring
    • Pre-Algebra Sessions >
      • :: Basic Division
      • :: Complex Division
      • :: Estimation Division
      • :: Division Practice Problems
    • Algebra II >
      • :: Cubic Equations
      • :: Complex Numbers
    • Chemistry >
      • Molarity Basics
    • C++ Sessions >
      • :: Introduction
      • :: Style v Syntax
      • :: Variables & Data Types
      • :: Intialize/Declare Variables
      • :: Types of Operators
      • :: Strings and Input - Output
      • :: How to Construct Arrays
  • AP Bio
    • :: Sketch Notes >
      • :: Part 1
      • :: Part 2
    • :: Chi-Squared Tests
    • :: Cancer
    • :: Hox Genes
    • :: Hardy-Weinberg Principle
    • :: Rule of Multiplication + Addition for Punnett Squares
    • :: CRISPR
    • :: Amino Acid
    • :: Peptide
    • :: Why study Peptides
    • :: Aquaporins
    • :: Gram Stains
    • :: Graph on Excel for Bio Lab
  • AP Chem
    • Organic Chemistry
    • I. Properties of Matter >
      • Neutralization
    • II. Periodic table >
      • Org of Periodic Table
      • :: Groups
    • III. Chemical bonding >
      • :: Mass to Mass conversion
      • :: Naming Acids
      • :: Cross Drop Charge
      • :: Predicting Products
      • :: Balance Equation Question
      • :: Learn to Balance Equation
      • :: VSEPR Simulation
    • IV. Molar Mass >
      • ::LR ER and excess reatant
      • :: Molecular/Formula Mass
      • :: Empirical Formula & Molar Mass
      • :: Percentages & Empirical Formula
      • :: Empirical formula
    • IV. Solutions and Solubility >
      • :: Types of Solutions with Solubility Curves
      • :: Solubility Curve
    • V. Easy Tricks and Tips >
      • :: Tip to Molecular Shapes
      • Memorizing Bond Angles and Polarity
      • :: Chemistry Formulas
      • :: Trick Polyatomic ions
    • VI. General AP Concepts >
      • :: Potential Energy Diagrams
      • :: Haber-Bosch
      • :: Le Chatelier
      • :: Pressure & Moles
      • ::Rydberg's Constant vs Unit of Energy
      • :: Equilibrium and RICE Tables
      • :: Kinetics
      • Galvanic Cells
    • :: Flash cards
    • :: VSEPR
  • AP Stats
    • Chi-Squared Tests
    • Applications of Statistics
    • Standardized Scores
    • Distributions Transformations
  • AP Calc
    • DI Method - Tabular Integration
    • Polar Curves: Tangent Line and Slope
    • Riemann Sums: Left and Right Approximations
    • :: Conic Sections Flash cards
    • :: Parent Functions Flash cards
    • Worked Out Problems >
      • :: Worked Out Problems I
      • :: Worked Out Problems II
      • :: Worked Out Problems III
      • :: Worked Out Problems IV
      • :: Worked Out Problems V
      • :: Worked Out Problems VI
      • :: Worked Out Problems VII
      • :: Worked Out Problems VIII
      • :: Worked Out Problems IX
      • :: Worked Out Problems X
      • :: Worked Out Problems XI
      • :: Worked Out Problems XII
      • :: Worked Out Problems XIII
    • Applying Trig Identities
    • L'Hopital's Rule
    • Differences Between Conic Sections
    • Graphing Conic Sections
    • :: Pre-Calc - Trig Identities
    • Tangent & Normal Lines
    • Indefinite integrals: U Sub
    • Calculus Derivatives >
      • Product Rule
      • Quotient Rule
      • Chain Rule
  • AP CS A
    • Studying for AP CSA 2020
    • :: Control Structures
    • :: What is Networking
    • :: Recursion
    • :: While Do While Loops in Java
    • :: Interface in Java
    • :: ArrayLists
    • :: Java Naming Conventions
    • :: Logic Circuits
    • :: Getters and Setters
  • AP Español
    • AP Español Salsa
  • Arduino
    • Quick Look
    • Project #1: Blinking LED
    • Project #2: Button LED
    • Project #3: Flowing LED
    • Project #4: LCD Display
    • Project #5: Serial Monitor
  • App
    • AP Go Pow How?
    • AP Go Pow APP Page
  • Musings
    • :: Backward induction
    • :: what is ISS
    • :: Rotational Matrices
    • :: Primary v Secondary Pollutants
    • :: Black Hole
    • :: Covid-19 Hackathon
    • :: Evolution of Immunizations
    • :: Predictions of Diseases
    • :: Book List
    • :: Patterncount
    • :: Binary Classification
    • :: Cybersecurity
    • :: Self Similarity
    • :: Trig Identities
    • :: UIL Number S
    • :: Box Offensive Play
    • :: Why Card Trick Works
    • :: Easy Multiplication
  • AP CREDIT
  • About