# math

## This Real-Life Infinite Fractal Zoom Shot Looks Like CGI, But It’s Real

In mathematics, a "fractal" is a never-ending pattern that remains similar across different scales, even infinitely. As seen with many computer-generated fractals, they can perpetually loop without any cuts or transitions. It's a mesmerizing effect.

## How Many Megapixels Do You Actually Need?

Camera resolution in the early 2000s was a space race to the biggest and best. Nikon ushered in the beginning of the end -- with the release of the 36-megapixel era-defining D800 -- to what became the resolution doldrums.

## From Bombs to Bubbles: Repurposing a 610mm Spy Plane Lens for Macro Photos

You didn’t ask to learn about bellows extension factors, but we're going to cover it with the most absurd camera that you may ever see!

## Lighting 101: Everything You Need to Know About Light Fall Off

Photographer Gavin Hoey recently produced a video for Adorama TV that tackles a critically important subject for photographers: light fall off. Mathematically captured by the so-called Inverse Square Law, it's vital that photographers understand this property of light, especially when working with strobes.

## Calculating the Distance of Wildlife in a Telephoto Shot

While enjoying a calm and misty morning at the pier in Malibu, California, I spotted dolphins. After observing them for a while, I noticed that their swimming was synchronized. There was a natural explanation for their circling: a feast had begun, quickly attracting sea lions, pelicans, and seagulls.

## How to Calculate Exposure Time with a 10-Stop ND Filter

Have you ever seen long exposure images shot using 10-stop ND filters? They are visually energetic and dynamic due to the motion blur caused by the moving clouds over a long duration of exposure.

## How to Use the ‘Divide’ Blend Mode to Instantly Remove Any Color Cast

Unmesh Dinda of PIXimperfect has put together a brilliant educational video on the oft-confusing Divide blend mode in Photoshop. In this tutorial he'll show you how to use it to remove any color cast, before diving into the fascinating mathematics behind this useful tool.

## Recreating the Look of 1850s Tintypes in Digital with Math and Science

While I was visiting San Francisco, Kristy Headley, a dear friend and fellow engineer, showed me her studio. There I was lucky enough to sit for her while she did some vintage tintyping. Tintyping was one of the earliest forms of photography, popular in the 1850s.

## Understanding Flash Guide Number (and Common Misconceptions)

Mystified by talk of "guide number" and "flash power"? Gerald Undone made this helpful 10-minute video that explains everything you need to know about the light from strobes and speedlights, from common misconceptions to practical formulas that will help you light your shots.

## How to Use Your Camera to Calculate the Speed of Earth’s Spin

Earth is spinning... and fast! It was during my first nights in astrophotography that it became very concrete for me. By taking pictures of the stars, one quickly obtains a change of star physiognomy that confirms the rotation of the earth. In this article, I describe how to use this phenomenon to measure the rotational speed of the earth with a simple camera.

## What is ‘Middle Gray’? Here’s a Short and Sweet Explanation

If you've never learned the technical details of what "middle gray" and "18% gray" are, check out this 6-minute video by Filmmaker IQ. John Hess shares the math and science behind the concepts to demystify them.

## The NPF Rule: A Formula for Sharp Star Photos Every Time

A common rule of thumb to figure out your maximum shutter speed for sharp stars at night is to divide 500 by your focal length. Sometimes it's called the 600 Rule or the 400 Rule or several other numbers that can be used depending on your sensor size. Unfortunately, it's a a very inaccurate rule today.

## Dispelling the Myths Around Depth of Field and Crop Factor

There is a lot of misunderstanding and confusion on the subjects of depth of field, the difference between full-frame and crop sensors, and the ‘crop factor.’

## The Math Behind How Digital Photo Resizing Works

When you resize (and resample) a photo in Photoshop, you’re given the option of strategies such as Nearest Neighbor and Bilinear. If you have no idea what those mean, check out this 9-minute video by Computerphile.

## This is How Cameras Glitch with Photos of Propellers

If you've ever photographed spinning airplane propeller or helicopter rotor blades with your smartphone, you may have found that the spinning blades were turned into bizarre shapes in the resulting photo. What you're seeing is distortion caused by a rolling shutter, when a CMOS sensor captures a scene by scanning across it very quickly rather than capturing the entire frame at once.

## A Look at the Math Behind Image Blurs and Filters

If you enjoy knowing the nitty gritty technical details of how photography technologies work, then you may enjoy the …

## How JPEG Handles Colors and Compression

Want to understand the math and science behind how JPEG files store your digital photographs? The YouTube channel Computerphile has a new series of videos on the JPEG. They're a bit long and heady, but you may find them interesting if you've ever wondered about the technical details behind one of the world's most popular image compression methods.

## This Free App Uses Your Smartphone’s Camera to Do Your Math Homework for You

Your smartphone's camera might fall short of the typical DSLR in just about every respect, but there is one thing it now do that not even your ultra-portable mirrorless camera can handle: your math homework.

No, we're not talking about shutting down the camera and opening your calculator app, what we're talking about is PhotoMath, a new app from MicroBLINK that uses your smartphone camera to solve equations for you.

## The Math Behind the Rolling Shutter Phenomenon

I remember seeing the photo above on Flickr once, and having my brain melt slightly from trying to figure out what went wrong.

The issue was the propeller was rotating as the camera detector ‘read out’, i.e. there was some motion during the exposure of the camera. This is an interesting thing to think about, lets have a look.

## A Mathematical Look at Focal Length and Crop Factor

I'm hoping this post can explain a lot of the confusion beginning photographers have about focal length and crop factors. Some understanding of basic geometry is required for you to fully grasp this post. Also note that I'll be rounding the math decently well. Just run through the calculations if you want exact answers.

## Momentum: Photos of Quantum Mechanic Calculations Scribbled on Chalkboards

For his project titled "Momentum", London/Madrid-based photographer Alejandro Guijarro spent three years visiting a number of the leading quantum mechanic research institutions of the world and photographed the chalkboards there exactly as he found them. The resulting photographs look like intelligent graffiti drawn by some of the brightest minds in science.

## The Economics of Leica Camera Pricing

Have you ever wondered how Leica chooses its pricing for its high-end cameras? J Shin has written up …