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What is a Chinese Character? - Not quite alphabet, word, or picture.
strokes make radicals, radicals make characters
character for cat
picture of a cat
discussion of the nature of Chinese Characters
You have probably seen enough Chinese characters to recognize that the picture on the lower right is not one, and the picture on the upper right possibly is. While it is sometimes said that Chinese characters are pictograms, not any picture will do. There are style rules that they must follow.
If you followed those style rules, could you create a new character? You could certainly create a plausible looking one. Your main difficulty would be to persuade people to adopt and use your new character. Plus, you would have minor technical difficulties in that there would be no Unicode representation of your new character. So, processing it on a computer would be problematic.
The English alphabet consists of 26 characters. So, it seems that as basic a question as, "How many Chinese characters are there?", would have a straight-forward answer. However, even that is a bit of a mystery. Chinese dictionaries are littered with thousands of characters that someone tried to invent, and have since fallen out of common usage. Sometimes someone will find a new use for one of these and give it a new life. (e.g. 囧 used to be a rather obscure character, but Chinese people started to use it as an emoticon. It since re-entered the language as an expression of displeasure.）
One needs to know somewhere between 2,000 and 3,000 characters to be competent at reading a Chinese newspaper, or modern book. Maybe, 6,000 characters would hold you in good stead for recognizing the vast majority of characters that are used in place, people and business names, etc.
In Mandarin, and I believe other Chinese dialects, one character always represents one syllable. Sometimes, one character will represent different syllables in different contexts, but it will always be just one syllable. (e.g. 行 is used in verbs and nouns. When it is used in nouns, it is pronounced "hang". In verbs it is pronounced "xing".） One to one correspondence with syllables is one of the few hard and fast rules I have found about Chinese characters. Even this is not true, when Chinese characters are used in other languages, such as, Japanese.
There are only a few hundred distinct syllables in any given spoken language. So, why are there thousands of characters? The answer is that the syllables can have different meanings in different contexts. In Chinese the relationship between a syllable and a word is a little different than in English. In English there are one syllable words, but most of the time, a single syllable doesn't have any meaning by itself. It needs to be combined with one or more other syllables to form a recognizable word. Conversely, in Chinese every syllable has a meaning by itself. The syllables around it may alter its meaning. For example, the Chinese word for contradiction, 矛盾， consists of one syllable that means, spear, and one syllable that means, shield. The characters that represent these syllables can also occur in other contexts, with their original meaning, though. You can probably imagine that with just a few hundred syllables, if every one means something, the same syllable will get reused in different contexts with a different meaning.
In spoken Chinese, the context of the speech disambiguates the meaning of the different syllables, but in written language, it is often helpful to have more information to clue the reader into the context the writer had in mind. I personally find Chinese written in a phonetic transcription of Chinese (pinyin) is difficult to read. Chinese people do，too.
Chinese characters have some interesting pros and cons, as a writing system. The obvious cons are that there are a lot of them. So, learning them takes more effort than learning an alphabet, it would be impossible to make a useful keyboard that had one character per key, and so on. The advantages, aside from cultural identity, are that Chinese characters are more versitile than an alphabet. Modern Chinese people can read poetry that was written more than a thousand years ago. People who speak different dialects, or even languages, can communicate in writing, even if they can't communicate verbally.
Next, I will explain the style rules for creating a Chinese character. My description of these rules is my own personal point of view, and doubtless an over-simplification, maybe even a little fanciful. However, I have found it to be helpful to my understanding of Chinese characters, and I hope others will too.
The atom of a Chinese character is a stroke. I have heard it said that 永 is the perfect character, because it contains exactly one of each of the basic strokes. It is arguable that there are actually several more basic strokes. For example, the vertical stroke might hook to the right, rather than the left, at the bottom. In any case, strokes are made with a single hand motion with a brush that is held vertically over paper. They are also relatively suitable for being carved, because they are made of straight lines with maybe one angular change in direction.
The molecule of a Chinese character is a radical, or simply a group of strokes that occur together in different characters. Some people would say that only some of these groups are radicals, but for simplicity, I will call them all that.
Given my definitions above, Chinese characters consist of one to maybe ten molecules/radicals, at most. There is a practical limit to the complexity of a character. More complex characters are harder to remember, and harder to fit properly in a fixed space, which is why I think an implicit upper bound exists.
The way you would make a new character would be to take an existing character and add another molecule/radicle to it. The picture at the top of this hub displays the four strokes that are used in the character for wood, 木. This character is used in many other characters, such as, 林，the character for a wooded area, which in turn is used in other characters, such as, 麻，the character for numb, which is used in 磨， a character for grinding, which is used in 蘑，a character for mushroom. At this point we are close to the limit of complexity for a character.
There is a link to a Web site, below, that tries to make use of these ideas to assist with looking up printed Chinese characters, and contains links to other resources for studying Chinese characters. You can copy paste characters from electronic documents into th Web site cited in the other link to look them up.