You are referring to "dendritic crystal growth formation," which happnes to be a very common crystal growth mechanism. At home kits simply have crystals that readily form at atmospheric pressure between a bit below freezing and not much higher than boiling water. These temperature limits are safely obtainable in an average home refrigerator freezer and stove top oven. Other, "more stubborn" crystals require pressure and temperature extremes only manageable in a laboratory or industrial plant.
I meantion all of this to inform you that the crystal growth mechanism does not typically (although it may!) depend on the environment the crystals form in. To answer your question, if the crystals in your kits do form dendrites, you can expect the fractaline patterns in their formation as you so astutely observed.
Want an even easier way to see dendritic crystal growth at home?
Get a bowl of ice cream that's fresh out of the freezer and a metal spoon. Put a small amount of spit (or water) into the concave portion of the spoon and spread out the liquid on the whole surface of the spoon. Press the convex portion into the ice cream, wait, and watch. Since water forms dendrites as it freezes, you can see fractal crystals grow right before your eyes. And of course, feel free to eat the ice cream afterwards!
Do fractals appear in home grown crystals? In order to answer this, we need to examine both what defines a fractal as well as what affects the crystallization process.A fractal is a geometric shape which can be broken into parts that are exact copies of the whole, but reduced in size. For beautiful examples and pictures of fractal designs, you can search online for Mandelbrot sets which are named after the man who studied and popularized fractals. However, he studied these in a mathematical sense, forming visualizations from equations. What chemists have found is that some crystals obey this property as well. In other words some crystals look the same when viewed at different magnifications because the pattern is repeated on different scales. (It is important to note that mathematically, fractals are infinite, as there is no limitation to how small or how big the design can get; however, in chemistry, there is a limit to this, as all crystals are made up of atoms of finite size.) Many of the crystals that we know of are geometric shapes. For instance, rock salt like we use on food is made up of sodium (Na+) and chloride (Cl-) ions which form cubes and rectangles. Diamonds made of carbon atoms also form beautiful geometric shapes. So how do we grow fractal crystals? This is largely dependent on the material you are crystallizing. Many polymers (long chains of repeating molecules) form fractals when they crystallize. There are ionic examples as well, such as sodium tartate, which can be grown into tree like structures. Now you are right to ask can they be grown at home, because many properties of a crystal depend on the conditions under which it is grown. Now I doubt that you will be synthesizing polymers at home, but I would say yes, you can grow fractal crystals at home. As an experiment, put a drinking glass into the freezer. Water will crystallize on the glass in a fractal pattern. You can also see this in snowflakes.
This is a very interesting question. I always thought fractals were really cool. If you are interested in more about fractals and interesting activities/experiments to do check out this site!fractals
As far as your question, fractal patterning should form on all crystals, even those grown at home at normal temperature and pressure. This site gives a little blurb about fractals in crystals. Now you can make some pretty cool crystals with bismuth (active ingredient in pepto-bismol) or potassium ferricyanide but these are possibly a little trickier than what you may be doing on your own at home because typically people use a saturated solution of something simple like regular old salt or sugar. Hope that helps!
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