The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable. "The" Mandelbrot set is the set obtained from the quadratic recurrence equation with , where points in the complex plane for which the orbit of does not tend to infinity are in the set. equal to any point in the set that is not a periodic point gives the same result. molecule by Mandelbrot. A plot of the Mandelbrot set is shown above in which values of in the complex plane are colored according to the number of steps required to reach . The adjoining portion is a circle with center at and radius The region of the Mandelbrot set centered around is sometimes known as the sea horse valley because the spiral shapes appearing in it resemble sea horse tails (Giffin, Munafo). Similarly, the portion of the Mandelbrot set centered around and
Box-and-Whisker Plots: Interquartile Ranges and OutliersBox-and-Whisker Plots: Interquartile Ranges and Outliers (page 3 of 3) Sections: Quartiles, boxes, and whiskers, Five-number summary, Interquartile ranges and outliers The "interquartile range", abbreviated "IQR", is just the width of the box in the box-and-whisker plot. That is, IQR = Q3 – Q1. The IQR is the length of the box in your box-and-whisker plot. (Why one and a half times the width of the box? Find the outliers, if any, for the following data set: To find out if there are any outliers, I first have to find the IQR. Outliers will be any points below Q1 – 1.5×IQR = 14.4 – 0.75 = 13.65 or above Q3 + 1.5×IQR = 14.9 + 0.75 = 15.65. Then the outliers are at 10.2, 15.9, and 16.4. The values for Q1 – 1.5×IQR and Q3 + 1.5×IQR are the "fences" that mark off the "reasonable" values from the outlier values. By the way, your book may refer to the value of "1.5×IQR" as being a "step". Find the outliers and extreme values, if any, for the following data set, and draw the box-and-whisker plot.
Using Body Awareness For Deeper Meditation & We The Change, Personal Development for Conscious People | Exploring How Self-Improvement Plays a Role in Global ConsciousnessI would like to share with you a very powerful meditation technique I use called ‘body awarenes s’. Even though this practice is primarily used during meditation, I have found great use in utilizing body awareness in my every day life as well. For those of you who already have a meditation practice, I highly recommend trying the following steps. For those of you who do not currently meditate, the practice brings a great sense of peace, joy, perspective and fulfillment into your life. I highly recommend you giving it a whirl and have written two excellent pieces on ‘meditation for beginners’. How To Meditate For Beginners20 Steps for Quieting The Mind Body awareness is extremely healthy and initiates the flow of fresh oxygenated blood to body areas that usually fall below the radar of your consciousness: Using the Body The big question for beginners is: where do I focus my attention during meditation? First, it is always helpful to make your practice of meditation ‘formal’. nostrils.
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